This course develops the mathematical techniques for the analysis of systems in the time domain.
An introduction to state space concepts and coordinate transformations is given, followed by solutions to
state space equations and advanced topics such as controllability and observability. This course is
very mathematical, but real-world examples will be given to bridge the gap between theory and practice.
TEXT: “Linear System Theory and Design,” Third Edition, by C.-T. Cheng, Oxford University Press, New York, NY, 1999.
State Space Modeling
Matrix representation
Definitions and Connections
Similarity Transformations
Jordan-Block Form
Multi-Input-Multi-Output Systems
Transmission Zeros
Linear Dynamical Equations
Solution of a Dynamical Equation
Impulse Response Matrices
Forced and Unforced Systems
Transition Matrix Properties
Stability of Linear Systems
Bounded-Input-Bounded-Output Stability
Asymptotic Stability
Lyapunov Stability Criterion
Controllability and Observability
Control and Observer Canonical Forms
Feedback Structures
Linear Systems Analysis
Controllability and Observability Grammians
Linearization of Systems
Superposition Concepts
Advanced Topics (time permitting)
Discrete-Time Systems
Control Issues
System Realizations
