Fall'06: EE 5231/AEM 8401

Linear Systems and Optimal Control

Course description Instructor and TA Texts/notes and software Grading policy

Introduction to dynamic systems and control. Fundamentals of matrix theory. Basic system properties: causality, linearity, time-invariance, finite dimensionality. Description of dynamic systems. State-space models. Solution to dynamics systems (discrete time, continuous time). Properties of state transition matrix. Similarity transformations. Modes of LTI systems. Laplace and Z transforms. Transfer functions. Lyapunov stability. Linearization. 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. Minimality. 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.

Class schedule: MWF 1:25pm - 2:15pm, Mechanical Eng. 212, September 5 - December 13

Instructor: Mihailo Jovanovic Office: EE/CSci 5-157 Office hours: MW 2:30pm - 3:30pm Phone: (612) 625 7870 E-mail: mihailo@umn.edu Web page: www.umn.edu/~mihailo

Teaching assistant: Fu Lin Office: EE/CSci 5-149 Office hours: Th 2:00pm - 4:00pm Phone: (612) 625 6839 E-mail: linxx242@umn.edu

Primary text	William L. Brogan Modern control theory Prentice Hall, Third Edition, ISBN 0-135-89763-7
Recommended text 1	Chi-Thong Chen Linear system theory and design Oxford University Press, Third Edition, ISBN 0-195-11777-8
Recommended text 2	Panos J. Antsaklis, Anthony N. Michel Linear systems Birkhauser, First Edition, ISBN 0-817-64434-2
Recommended text 3	Wilson J. Rugh Linear system theory Prentice Hall, Second Edition, ISBN 0-134-41205-2
Class notes	Will be provided on a fairly regular basis
Software	Homework sets will make a use of Matlab and Simulink

Homework (20%), Midterm exams (2 x 25%), Final exam (30%)

Homework policy: Homework is intended as a vehicle for learning, not as a test. Moderate collaboration with your classmates is allowed. However, I urge you to invest enough time alone to understand each homework problem, and independently write the solutions that you turn in. Homework is generally handed out every Friday, and it is due at the beginning of the class a week later. Late homework will not be accepted. Start early!

Tentative exam schedule: Midterm 1: October 4; Midterm 2: November 8; Final: during exam week.