Course Details
Subject {L-T-P / C} : EE6301 : Linear System Theory { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Asim Kumar Naskar
Syllabus
| Module 1 : |
Solution of homogeneous ODE. Dependent and independent solution. Existence and uniqueness of solution. ODE solution in State Space. Concept of set, space, and vector space. [6Hrs]
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| Module 2 : |
State space representation of different dynamical systems from the first principle: Linearization, equilibrium point, and stability. [4Hrs] |
| Module 3 : |
Solution of autonomous, non-autonomous, time-varying, and time-invariant systems. Fundamental matrix, state transition matrix. State Space realization. [4Hrs]
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| Module 4 : |
Range and Null space of a matrix. Linear combinations and the concept of Basis. Gramm-Smith Orthogonalization. [4Hrs]
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| Module 5 : |
System Analysis: Controllability, Observability, Similarity Transforms, Invariant Subspaces, Kalman decomposition, Stabilizability and Detectability, Duality. Balanced realization and Model Order Reduction. Poles and Zeros of MIMO systems. [10Hrs]
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| Module 6 : |
State Variable Feedback for Single- and Multivariable Systems. Concept of optimal control and solution of the linear quadratic regulator. [5Hrs]
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| Module 7 : |
State observer, reduced order observers, and combined observer-controller system. [3Hrs] |
Course Objective
| 1 . |
Students will be briefly introduced to modern control theories, techniques, and tools for analyzing linear dynamical systems. Key topics include the solution of the state equation, state transition matrix, controllability, observability, and other related properties. |
| 2 . |
Students will be briefly introduced to pole placement design, state observers, stability analysis, etc. |
| 3 . |
Students will be introduced to different toolboxes available in MATLAB and Mathematica to solve, analyze, and visualize control system problems. |
Course Outcome
| 1 . |
At the end of the course, students will be able to apply the concept of solvability, dependence, and independence of solutions of ordinary differential equations.
|
| 2 . |
At the end of the course, students will be able to model various dynamical systems in a linear state-space form. |
| 3 . |
At the end of the course, students will be able to solve autonomous and non-autonomous linear dynamical systems. |
| 4 . |
At the end of the course, students will be able to realize SISO and MIMO transfer functions. |
| 5 . |
At the end of the course, students will be able to analyze systems using concepts of controllability, observability, invariant subspaces, and control-invariant subspaces. |
| 6 . |
At the end of the course, students will be able to design various state feedback control laws for SISO and MIMO systems, as well as design full-order and reduced-order observers. |
| 7 . |
At the end of the course, students will be able to utilize software tools in MATLAB and Mathematica to solve, analyze, and visualize control systems, demonstrating proficiency in simulation and the interpretation of results. |
Essential Reading
| 1 . |
C. T. Chen, Linear system theory and design, Oxford Univ. Press , 1998 |
| 2 . |
P. J. Antsaklis, A. N. Michel,, Linear Systems, Birkhauser , 2009 |
Supplementary Reading
| 1 . |
J.S.Bay, Fundamental of Linear State Space Systems, MacGraw-Hill , 1999 |
| 2 . |
Wilson J. Rugh, Linear system theory, Pearson , 1995 |
Journal and Conferences
| 1 . |