EE/AEM 5231 – Linear Systems and Optimal Control
Mihailo Jovanovic, University of Minnesota, Fall 2013
Introduction to dynamic systems and control. Basic system properties: causality, linearity, time-invariance. Description of dynamic systems. State-space models. Linearization. Solution to dynamics systems (discrete time, continuous time). Properties of state transition matrix. Similarity transformations. Modes of LTI systems. Laplace and Z transforms. Impulse response; transfer function; frequency response. Lyapunov stability for LTI systems. Signal measures and input-output stability. Input-output norms. Interconnections: stability and performance. Controllability – basic ideas. Controllability – standard and canonical forms, modal tests, etc. Observability, observability tests. Kalman-Ho algorithm for identification of LTI systems. Realization theory for LTI systems. Kalman decomposition. Multivariable poles and zeros. Interconnections: minimality, well-posedness, stability. State-feedback design. Pole placement. Linear Quadratic Regulator (LQR) design. Algebraic Riccati Equation. Observer design and filtering. Observer-based controllers. Separation principle. Tracking and disturbance rejection. Uncertainty and rudiments of robustness.
TuTh, 11:15am - 12:30pm, MechE 108; Sept 3 - Dec 11, 2013
Instructor and Teaching Assistant
Textbook and software