### MA 5311 Linear Systems Theory

#### Course Details

Introduction: Physical systems, models and representations.

Linear system representation: Definitions, state transition map, response map, impulse response matrix, adjoint equations, linear quadratic optimization, applications.

Linear time invariant systems: General properties, minimal polynimial, decomposition theorem, the linear map X—› AX+XB.

Stability: Input-output stability, state related stability concepts and applications.

Controllability and Observability: Controllability and observability of dynamical systems, Controllability of the pair (A(.),B(.)), observability of the pair (C(.),A(.)), duality, Kalman decomposition theorem, minimal realization, controllable canonical form.

Linear state feedback and estimation: Linear state feedback, linear output injection and state estimation, feedback of the estimated state, infinite time horizon linear quadratic optimization.

#### Course References:

Text Books:

1. L.A. Zadeh and C.A. Desoer, Linear System Theory: The state space approach, Dover, 2008.

Reference:

1. P.J. Antsaklis and A. N. Michel, Linear Systems, Birkhauser, 2005.

2. Chi-Tsong CHen, Linear System Theory and Design, Oxford Univ Press, 3rd edition, 1998.

3. W. J. Rugh, Linear System Theory, Prentice Hall, 2nd edition, 1995.

4. T. Kailath, Linear Systems, Prentice Hall, 1980.