ELE 514E - System Theory

Course Objectives

Understanding basic concepts in linear systems theory
Modelling systems using linear state-space representation
Obtaining the solutions of linear systems
Understanding qualitative properties of linear systems

Course Description

This course is an introduction to linear systems theory. Basic concepts like state transition matrix, controllability, observability, minima realization are introduced and students should provide a proof of their understanding in homeworks that contain anayltical proofs as well as MATLAB exercises.
CONTENTS:
General definition of dynamical systems
Linearity and time-invariance
State-space representations of linear systems
Quantitative analysis of linear systems:
Solutions to LTV systems
Solutions to LTI systems
Linearization of nonlinear systems around a nominal solution
Qualitative analysis of linear systems:
Stability
Controllability and state feedback
Observability and output feedback
Realization and minimal realization
Geometric theory of linear systems
Controllable and observable subspaces
Stabilizability conditions in terms of