EE/AEM 5231 – Linear Systems and Optimal Control

Mihailo Jovanovic, University of Minnesota, Fall 2013

Course description

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.

Class schedule
TuTh, 11:15am - 12:30pm, MechE 108; Sept 3 - Dec 11, 2013

Instructor and Teaching Assistant

  • Instructor
    Mihailo Jovanovic
    Office: Keller Hall 5-157
    Office hours: Tu 12:30pm - 1:30pm (or by appointment)

  • Teaching Assistant
    Xiaofan Wu
    Office: Keller Hall 2-276
    Regular office hours: Wednesday, 2pm - 3pm
    Extra office hours: Monday, 2pm - 3pm (only when HW is due Tuesday)

Textbook and software

  • Textbook
    Joao P. Hespanha
    Linear Systems Theory
    Princeton University Press, First Edition, ISBN-10: 0-691-14021-9

  • Software
    Homework sets will make a use of Matlab and Simulink

Grading policy

  • Homework (40%)
    Midterm exam (30%)
    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 Wednesday, 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: Oct 24
    Final: during exam week