Mathematics and Physics play an important role in understanding the fundamental laws of nature and it directly correlates the other fields of engineering and natural sciences. Understanding the importance and necessity of acquiring knowledge about the most exciting and interesting branch of science and engineering, Department of Mathematics and Physics belongs to the School of Engineering and Physical Sciences.
The Department of Mathematics and Physics is one of the dynamic departments of North South University, which incorporates fundamental, experimental and mathematical study. We are committed to excellence in teaching and research. All our faculty members are highly qualified and they are responsible for teaching the Mathematics, Physics and Statistics courses offered by the University. Twelve of our sixteen full-time faculty members are Ph.D. s from North America or Western Europe. The breadth of expertise of our faculty members covers almost the entire range of mathematics and physics, pure as well as applied. They are active in all branches of state-of-art research which include, but not limited to, the following topics:
Department of Mathematics and Physics (DMP), North South University (NSU), celebrated the pi-moment of the century at the campus. Pi is the ratio of the circumference of a circle to its diameter. It is symbolized by the greek letter pi in the lower case (π). This is a fixed quantity, which is usually taken to be 3.14. The number of digits after the decimal is infinite. In the western countries, especially in the US, March 14 (written 3/14 in the American style) is celebrated every year as the pi-day. March 14 this year is a bit more special. The first ten digits of the value of pi, i.e., 3.141592653 can be arranged as March 14, 15, 9:26:53. We call this special moment as the pi-moment. This moment will come again in 2115, one hundred years later.
At this precise moment (according to Bangladesh-time) of this century, students from various departments of NSU participated in a celebration of the moment. They formed a human circle with a diameter. Then dividing the number of people in the circumference by the number of people in the diameter yielded a value close to the actual value of pi. They did the same thing with chairs. At the end a large number of people formed the shape of the symbol π.
Professor Partha Pratim Dey, the chairman of the Department was present at the event along with a few other faculty members, namely, Kazi Abu Sayeed, Hasina Akter, and Muhammad Asad-uz-zaman. A few part time faculty members were present as well as Golam Dastegir Al Quaderi, a faculty member of the Physics Department at Dhaka University, who participated as a guest. The initiative was taken by Naureen Ahsan, a part time faculty member at NSU and a full time faculty member at Dhaka University. 
Pi-moment of the century, March 14, 15 9:26:53
Chairman of DMP is seen with faculty members and students.
The human circle yielded a close value to pi A chair circle yielded an even closer value to pi
A human pi symbol
| Name of Fculty | Area of Research |
| Dr. Partha Pratim Dey | Coding Theory, Mathematical Modeling |
| Dr. Miftahur Rahman | Control Systems and CNC Machine |
| Dr. Abu M Khan | Theoritical High Energy Physics |
| Dr. Mamun Molla | Computational Fluid Dynamics, Parallel Computing |
| Dr.Mohammad Sahadet Hossain | Systems and Control Theory, Model Order Reduction, Scientific Computing |
| Dr. Subir Chandra Ghosh | Nanometarils and Solar Energy |
| Dr. Muhammad Asad-Uz-Zaman | Nonlinear Dynamics |
| Dr. Hasina Akthar | Dynamical Systems and Ergodic Theory |
| Dr. Mohammad Monir Uddin | Systems and Control Theory, Model Order Reduction, Numerical Liner Algebra and Scientific Computing |
| Md. Zahangir Hossain | Computational Fluid Dynamics |
| Projects | Coordinators |
| Reduced order modeling of periodic control systems with application to circuit problems |
Dr.Mohammad Sahadet Hossain |
| Structure Preserving Model Reduction of Large-Scale Second Order Dynamical Systems Using the PDEG Method and Application to Some Real Problems |
Dr. Mohammad Monir Uddin |
• Lattice Boltzmann Simulation of Airflow and Heat Transfer in a Model Ward of Hospital; M. F. Hasan, T. A. Himika, M. M. Molla ; J. Thermal Science and Engineering Applications, Vol. 9, 011011-1, 2017, DOI 10.1115/1.4034817.
• Structure preserving model order reduction using the projection onto the dominant Eigen-space of the Gramian (PDEG) ; M. M. Uddin; in international conference on Electrical, Computer and Communication Engineering (ECCE ), IEEE, 2017, pp. 197--202, 2017.
• Efficient techniques to solve the periodic projected Lyapunov equations and model reduction of periodic systems ; M. Sahadat Hossain and M. M. Uddin; Mathematical Problems in Engineering, Vol. 2017, 2017, 11 pages.
• Structure preserving iterative methods for periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems; P. Benner, M. Sahadet Hossain; Numerical Algorithms (Springer), pp. 1-24, 2017, DOI 10.1007/s11075-017-0288-y.
• On [6,4] Error Correcting Codes over GF(7); P. Dey and Toyarak Rian; International Journal of Computer and Information Technology, Vol. 06, 2017, pp. 19-26
• Equivalence of Error-Correcting Quaterrnary [6,3] Self-Dual Codes ; Farzana K. Elora and P. Dey ; Journal of Information Science and Optimization, Vol. 38, 2017, pp. 585-601
• On Quinary Error-Correcting [6,4] Codes; P. Dey, A. K. Ghosh; Journal of DiscreteMathematical Sciences & Cryptography, Vol. 19 (2), pp. 405-411, 2016
• Large-Eddy Simulation of Pulsatile Flow through a Channel with Double Constrictions; M. M. Molla, M. C. Paul; Fluids, Vol 2017 (2), pp. 1-19 (2016).
• Prediction of Heat Transfer to Fully-Developed Pipe Flows with Modified Power-law Viscosity Model Fluid ; M. M. Molla, S. G. Moulic, L-S Yao; Journal of Mechanics, Vol. 1(1), pp.1-47, 2016.
• Lattice Boltzmann simulation of airflow and mixed convection in a general word of hospital ; T. A. Himika, M. F. Hasan, M. M. Molla; J. Engineering Computation, Vol. 2016, 15 pages, 2016.
• Natural convection flow of Nanofluid along a vertical wavy surface; F. Habiba, M. M. Molla, M. A. H. Khan; AIP Conf. Proc. 1754, 050018, 2016.
• Natural convection flow in porous enclosure with localized heating from below with heat flux ; M. N. A. Siddiki, M. M. Molla, S. C. Saha; AIP Conf. Proc. 1754, 050016 (2016).
• Natural convection of non-Newtonian fluid along a vertical thin cylinder using modified power-law model; S. Thohura, M. M. Molla, M. M. A. Sarker; AIP Conf. Proc. 1754, 040021, 2016.
• Large-eddy-simulation of air flow and heat transfer in general ward of hospital using lattice Boltzmann method; F. Hassan, T. Himika, M. M. Molla; AIP Conf. Proc. 1754, 050022 (2016)
• Model Reduction of Time-Varying Descriptor Systems:Numerical Methods, Algorithms, and Applications; Mohammad Sahadet Hossain; Publisher: Scholars' Press, Germany.ISBN: 978-3-659-84001-2
• Projection-Based Model Reduction for Time-Varying Descriptor Systems: New results; Mohammad-Sahadet Hossain; Numerical Algebra, Control and Optimization (NACO); Publisher-American Institute of Mathematical Sciences(AIMS), vol. 6(1), pp. 73-90, 2016.
• Structure preserving mor for large sparse second order index-1 systems and application to a mechatronic model ; P. Benner, J. Saak, and M. M. Uddin; Mathematical and Computer Modelling of Dynamical Systems, Vol. 22 (6), pp. 509-523, 2016.
• Balancing based model reduction for structured index 2 unstable descriptor systems with application to ow control ; P. Benner, J. Saak, and M. M. Uddin; Numerical Algebra, Control and Optimization (AIMS), Vol. 5(1), pp. 1-20, 2016.
• Reduced-order modeling of index-1 vibrational systems using interpolatory projections ; P. Benner, J. Saak, and M. M. Uddin; in 19th International Conference On Computer and Information Technology (ICCIT), IEEE. pp. 134-138, 2016.
• Rational Krylov subspace method (RKSM)for solving the Lyapunov equations of index-1 descriptor systems and application to balancing based model reduction ; M. M. Uddin, M. S. Hossain and M. F. Uddin; in 9th International Conference on Electrical and Computer Engineering, IEEE, pp. 451- 454, 2016.
• Parametric study on thermal performance of horizontal earth pipe cooling system in summer; S. F. Ahmed, M. T. O. Amanullah, M. M. K. Khan, M. G. Rasul, and N. M. S. Hassan; Energy Conversion and Management, vol. 114, pp. 324-337, 2016.
• Lax Pairs and Integrability Conditions of Higher-Order Nonlinear Schr ̈odinger Equations; M. Asad-uz-zaman, H. Chachou Samet, U. Al Khawaja; Communications in Theoretical Physics, Vol. 66(2), 2016.
Department of Mathematics and Physics (DMP) offers following twenty three (23) courses:
| Code | BUS112 |
| Credit hours | 0 |
| Textbook |
|
| Pre-requisites | High School Mathematics. |
| Course Content | Fundamentals of Algebra: Real Numbers, Fundamentals of Algebra: Exponents, Polynomials, Fundamentals of Algebra: Factoring, Rational expressions, Radicals, Linear equations, Formulas and Applications, Quadratic equations, Other types of Equations, Inequalities, Cartesian Co-ordinate systems, Graphing Relations, Functions, Linear Functions, Equations of a line, Symmetry, Algebra of Functions, Inverse Functions, Quadratic Functions, Synthetic Division, Exponential Functions, Logarithmic Functions, Equations on Exponential and Logarithmic functions, Systems of Equations, Systems of Inequalities; Linear Programming, Matrix Solution of Linear Systems, Properties of Matrices, Determinants, Cramer's rule, Matrix Inverse. |
| Code | MAT116 |
| Credit hours | 0 |
| Textbook |
|
| Pre-requisites | High School Mathematics. |
| Course Content | Behavior of functions in some depth including properties, graphs, inverses, transformations, and compositions. This course pays particular attention to linear, quadratic, polynomial, rational, exponential, and logarithmic functions. It covers trigonometric functions and inverse trigonometric functions as well. |
| Code | MAT120 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT116. |
| Course Content | Tangent lines; limits and continuity; differentiation: definition, basic rules, chain rule, rules for trigonometric, inverse trigonometric, exponential and logarithmic functions; implicit differentiation; rates of change, related rates problems, linear approximation and differentials; L'Hospital's rule; concepts of local and absolute maximum and minimum including first and second derivative tests; integration: definition, anti-differentiation, area; integration by simple substitution; Fundamental Theorem of Calculus. |
| Code | MAT125 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT116 or an adequate test score. |
| Course Content | Homogeneous and Nonhomogeneous System of Linear Equations, Echelon form, Gaussian Elimination Method (unique, infinite numbers and no solutions)Properties of Determinants, Determinant by Cofactor Expansion, Evaluating Higher Order Determinants by Row Reduction, Cramer’s Rule .Matrices and Matrix Operations, Transpose, Properties of Transpose, Triangular, Symmetric and Skew Symmetric Matrices, Inverse, Properties of Invertible Matrices,Method of Finding the Inverse of a Matrix, Further Results on System of Linear Equations using Inverse Matrix Technique, Rank .Introduction to Vectors, Vector addition and Scalar multiplication, Norm of a vector, Dot Product, Projections, Euclidean n-Space, Real Vector Space, Subspace, Linear Combinations, Linear Dependence and Independence, Spanning Set, Basis, Dimensions, Solution Space, Null Space, Rank and Nullity. General Linear Transformation, Kernel and Image of Linear Mapping, Rank and Nullity of Linear Mapping. Eigenvalues and eigenvectors, Cayley Hamilton Theorem, Diagonalization.Geometric Linear Programming, Applications in Business and Economics. |
| Code | MAT130 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT120. |
| Course Content | Area between two curves, Length of plane curves, Area of surface of revolution, Volumes by slicing disks and washers, Volumes by cylindrical shells, Hyperbolic functions and hanging cables & Integrations. Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integrating rational functions by partial fractions, Improper integrals.Polar coordinates, Area in polar coordinates, Tangent lines and arc length for parametric and polar curves, Conic sections in calculus. |
| Code | MAT240 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT130. |
| Course Content | Sequences, Monotone Sequences, Infinite Series, Convergence Test, The Comparison, Ratio, and Root Tests, Alternating Series; Conditional Convergence, Maclaurin and Taylor Polynomials, Maclaurin and Taylor Series; Power Series.Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces , Vectors, Dot Product; Projections, Cross Product, Parametric equations of lines, Planes in 3-space, Quadric Surfaces, Cylindrical and Spherical Coordinates.Introduction to Vector Valued Functions, Calculus of Vector Valued Functions, Change of Parameter; Arc length, Unit Tangent, Normal, and Binormal Vectors, Curvature. |
| Code | MAT250 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT130 |
| Course Content | Infinite Series, Vector Valued Functions, Functions of two variables, Limit and Continuity, Partial Derivatives. Differentiability and Chain Rule, Directional Derivatives and Gradients.Tangent Planes and Normal Vectors, Maxima and Minima of Functions of two variables, Double Integrals over rectangular regions, Double Integrals over non-rectangular regions. Double Integrals in Polar Coordinates, Triple Integrals, Centroid, Center of Gravity, Change of variables in Multiple Integrals; Jacobean. Triple Integrals,Vector fields and vector valued function, Line integrals, Green’s Theorem, Surface Integrals, The Divergence, Theorem, and Stokes Theorem. |
| Code | MAT350 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | Complex analysis, Fourier series and transforms, Laplace transforms and the solution of ordinary differential equations, in particular Bessel function and Legendre polynomials. |
| Code | MAT361 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | Basics of elementary probability theory; discrete and continuous random variables along with their probability distributions(cumulative distribution function; expected values and variance); special random variables: Bernoulli, binomial, geometric, negative binomial, Poisson, hyper-geometric, uniform, exponential and normal distributions);multivariate distributions(joint distributions; marginal and conditional distributions; covariance and correlation); descriptive statistics and sampling distribution of statistics;parameter estimation by moment and maximum likelihood method; comparing the performance of estimators using properties of unbiasedness, efficiency and minimum variance; confidence interval estimation for the mean and difference of two means; hypothesis testing on mean and difference of two means. |
| Code | MAT370 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | The Real Numbers, Sequences, Limits, Continuity and Uniform Continuity of Real Variable Functions, Differentiation, The Sequences of Functions and their Convergence, The Riemann Integral, Fundamental Theorem of Real Calculus and its Proof, Complex Variable Functions, Limits and Continuity of Complex Functions, Derivative, Analyticity, Cauchy-Riemann Equations, Fundamental Theorem of Complex Calculus and its Proof. |
| Code | MAT480 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | Introduction to Differential Equations, First-order Differential Equations, Applications of first order Differential Equations, Linear Differential Equations of higher-order, Applications of second-order Differential Equations with variable coefficient, Systems of Linear Differential Equations. |
| Code | MAT490 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | Laplace Transform, Existence of Laplace Transform, Inverse Laplace Transform, Laplace Transform of Derivatives and Integrals, Shifting on the s-axis, Shifting on the t-axis, Differentiation and Integration of Laplace Transform, Convolution, Inverse Laplace Transform of partial Fractions, Inverse Laplace Transform of periodic Functions, Fourier Series FS for Functions of Period 2p or arbitrary period, Fourier Series for Even and odd Functions, Half-Range Fourier Expansion, Determination of Fourier Coefficients without Integration, Fourier Approximations and minimum square error, The Fast Fourier Transform, Complex Variable Functions, Limits and Continuity, Derivatives, Analyticity and Cauchy-Riemann Equations, Conformal Mapping, Relation between Analyticity and Coformality, Mobius and other Transformations, Complex Integrals, Cauchy Integral Formulae, Taylor’s Series, Singular Points, Laurent’s Series, Residues and Residue Theorem, Evaluation of Real Definite Integrals using Complex Integrals. |
| Code | MAT495 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT250 |
| Course Content | Sets and Equivalence Relations, Semigroups&Monoids, Free Semigroup& Free Monoid, Congruence Relations and Quotient Structures, Fundamental Theorem of Semigroup Homomorphism, Groups, Sn, Zn, Subgroups, Normal Subgroups, Generating Sets, Generators, Fundamental Theorem, Lagrange’s Theorem, Quotient Group, Cyclic Subgroups, Generating Sets, Generators, Fundamental Theorem of group Homomorphism, Rings and Ideals, Fundamental Theorem of Ring Homomorphism, Integral Domain, Principal Ideal Domain, Divisibility in Integral Domain, Unique Factorization Domain, Field, K [T]- the polynomials over a field K, K [t] as a Principal Ideal Domain and Unique Factorization Domain, Fundamental Theorem of Algebra, Ordered Sets and Lattices, Principle of Duality, Bounded Lattices, Distributive Lattices, Complemented Lattice. |
| Code | PHY105 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | None |
| Course Content | Vectors, equations of motions, Newton’s laws, conservation laws of energy, linear momentum, Work-Energy theorem, extension of linear into rotational motion including the conservation laws, gravitation, simple harmonic motion, travelling waves, calorimetry, thermal equilibrium, 1st and 2nd laws of thermodynamics. |
| Code | PHY105L |
| Credit hours | 1 |
| Textbook |
|
| Pre-requisites | PHY105 |
| Course Content | Introduction to Measurements and Statistical Error, Force table, Atwood machine, Hook’s law, Mass-spring oscillation, Simple pendulum, Compound pendulum and Static equilibrium. |
| Code | PHY107 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT120 and Physics in HSC/A Level |
| Course Content | Vectors, equations of motions, Newton’s laws, conservation laws of energy, linear momentum, Work-Energy theorem, extension of linear into rotational motion including the conservation laws, gravitation, simple harmonic motion, travelling waves, calorimetry, thermal equilibrium, 1st and 2nd laws of thermodynamics. |
| Code | PHY107L |
| Credit hours | 1 |
| Textbook |
|
| Pre-requisites | PHY107 |
| Course Content | Introduction to Measurements and Statistical Error, Force table, Atwood machine, Hook’s law, Mass-spring oscillation, Simple pendulum, Compound pendulum and Static equilibrium. |
| Code | PHY108 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT130 and PHY107 |
| Course Content | Electricity and Magnetism: Coulomb’s Law,Electric field and Gauss’s Law, Potential, Capacitance field, Magnetic forces,Induced Electromotive force,AC circuit.Electric Field and Potential:- Conceptually, Electric Field and Potential:- Discrete System , Electric Field and Potential:- Continuous System, Electric Field and Potential:- Gauss’s Law, Capacitors and Capacitance, Dielectric, Ohm’s Law, Circuit Theory, Magnetic Force I, Magnetic Force II, Biot-Severt Law, Ampere’s Law, Inductance I, Inductance II, Alternating Fields and Current I, Alternating Fields and Current II, Maxwell’s Equation, Magnetic Properties of Matter. |
| Code | PHY108L |
| Credit hours | 1 |
| Textbook |
|
| Pre-requisites | PHY108 |
| Course Content | Introduction to electric equipment, Verification of Ohm’s law, Charging and Discharging of capacitor, Time constant of a Circuit with resistor and capacitor in series and Magnetic induction. |
| Code | BSC201 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | None |
| Course Content | Representation of functions numerically, graphically and algebraically, linear, quadratic, polynomial, rational, root/power, piecewise-defined, exponential, logarithmic, trigonometric and inverse trigonometric functions. The algebraic structure and graph of a function, intercepts, domain, range, intervals on which the function is increasing, decreasing or constant, the vertex of a quadratic function, asymptotes. Concept of heat, temperature, laws of thermodynamics, and different types of thermal processes. The kinetic theory of gases, specific heat of ideal gases, Maxwell’s laws of equi-partition of energy and related problems. |
| Code | MAT140 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT230 |
| Course Content | Probability and the laws of probability. Conditional probability. Independence. Expectation. Discrete and continuous distributions. Point and interval estimation. Regression and Correlation. Illustrations from Engineering. |
| Code | MAT230 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT130 |
| Course Content | Linear Algebra: Definition of matrix. Algebra of matrices. Multiplication of matrices. Transpose of a matrix and inverse of matrix. Rank and elementary transformation of matrices. Solution of linear equation. Linear dependence and independence of vectors. Matrix polynomials. Determination of characteristic roots and vectors. Null space and nullity of matrix. Quadratic forms.Vector Analysis: Vectors: Scalar and vector products and associated geometrical interpretation. Vector field, gradient field, divergence and curl of a vector field, Line integral, Green’s theorem, Surface integral, Divergence theorem, Stokes’ theorem. |
| Code | MAT260 |
| Credit hours | 3 |
| Textbook |
|
| Pre-requisites | MAT130 |
| Course Content | efinition of ordinary differential equation, Solution of first order ordinary differential Equations by various methods, Solution of second order ordinary differential equations with constant coefficients, Series solutions of ordinary differential equations by power series and Frobenius series, Solution of Bessel’s equation and Legendre’s equation. Definition of partial differential equations, Derivation of classical partial differential equations and their solutions. |
Tasmia Rahman Shahidi, from the department of ECE and Tasfea from Civil and Environmental Engineering, respectively won the 4th and 7th position in the 2nd Women's Mathematics Olympiad 2018. The competition was organised in cooperation with Department of Mathematics, the University of Dhaka and Women’s Mathematics Olympiad Committee and A. F. Mujibur Rahman Foundation. 180 students from 20 different universities from all over the country participated. Honourable faculty members from the Department of Mathematics, University of Dhaka judged the event. The winner from NSU has praised their faculties for being supportive and to encourage them to participate in such activities. Ms Tasmia said 'Mathematics is one of her favourite subjects and Dr. Hasina Akhter, faculty of Mathematics department at NSU specially guided her for the event. Rather than testing students’ ability to recall facts, the competition was designed to test students’ mathematical creativity and their ability to formulate and defend their conclusions. Every student has some potential abilities and skills, participating in different competitions is one of the ways to hone the skills and take one to the next level.
The Department of Mathematics and Physics is located on the 10th floor of the SAC building. It does not offer an undergraduate degree like a Bachelor of Science degree in Mathematics or Physics yet. It is because the department came into existence only six months ago. However, the department serves a significant number of students through a wide range of service courses. It primarily imparts the mathematics and physics training for the undergraduate students of the university. The department also runs a thirty–credit minor program in mathematics.
Currently we have full-time and part-time faculty members in our department. Ten of our thirteen full-time faculty members are Ph.D. s from North America or Western Europe. The part-time faculty members are from among the best faculty members of the reputed universities in Dhaka like Dhaka University, Bangladesh University of Engineering and Technology etc. The breadth of expertise of our faculty members covers almost the entire range of mathematics and physics, pure as well as applied.
We have a plan to transform our department from present service position to a full-fledged Department of Mathematical Sciences, which among other things will offer a major in mathematics as well as a major in Physics. I believe, given our faculty strength, this transformation should be a piece of cake.
Partha Pratim Dey
Professor & Chair
Department of Mathematics and Physics (DMP)
Title: Efficient Reduced Order Modeling of Periodic Control Systems with Application to Circuit Problems.
Abstract:
In this seminar, we have presented a method for the model order reduction of continuous linear time-varying (LTV) periodic descriptor systems where the system's matrices are singular. This model order reduction strategy is based on the linear time-invariant (LTI) reformulation of the LTV model through suitable discretization scheme. The resulting linear time-invariant (LTI) system is then reduced using balanced truncation model reduction method. We use the Low-Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration to approximate the solutions of the corresponding time-invariant Lyapunov equations. Due to the singularity of the system's matrices, we have used the Pseudo-inverses to find the optimal shift parameters that are used in LRCF-ADI approximation. The step responses, bode plots and eigenstructures of both the original and reduced system are compared to show the accuracy of the proposed model reduction approach.
Postal Address:
Department of Mathematics and Physics
North South University
Plot 15, Block B
Bashundhara,
Dhaka 1229
Bangladesh
PABX: +880 2 55668200 (Ex- 1561)
Fax: +880 2 55668202
Email: info_dmp@northsouth.edu
Website: http://www.northsouth.edu/academic/seps/dmp.html