AAE 56400: Systems Analysis and Synthesis


State space methods of analysis and design of continuous and discrete-time linear systems. Coordinate transformations, Jordan canonical forms, digital control, controllability and observability of continuous and discrete systems. Liapunov stability analysis. The linear regulator problem of optimal control via Hamilton Jacobi theory. Pole assignment, stabilizability, detectability. State estimation for deterministic models. Minimal order observers.

Format: 3 hrs lecture per week

Credit hours: 3

Status: Elective, Dynamics and Controls

Offered: Fall

Pre-requisite: AAE 364 or equivalent

Co-requisite: MA 511 recommended concurrently

Course Instructor: M. Corless

Text: Notes for AAE564, M. Corless

Assessment Method: Two exams (70%), Homework/Project (30%)

Course Objective:


To provide the student with the basic concepts and techniques used in the analysis and control design of linearizable systems.

Objectives include developing abilities to:

Develop state space and transfer function models of physical systems

Analyze a system for stability, controllability, and observability

Design feedback controllers for stability, performance requirements, and disturbance rejection

Necessary Background: Linear algebra, differential equations, and maturity

Topics (number of Lectures):

State space modelling of physical systems


Transfer functions and their state space realizations

Behaviour of linear systems: modes, state transition matrices


Lyapunov techniques for stability analysis

Controllability and observability

State feedback controllers and stabilizability

Observers and detectability

Output feedback controllers

Disturbance rejection and output tracking

Linear quadratic optimal controllers

Application to aerospace/mechanical systems

Relationship of course to program objectives:

1) The course provides the fundamental concepts and techniques for the analysis and control design of linearizable systems.

2) Homework assignments develop students' abilities to solve problems, including open-ended and design problems (2a). These assignments also improve ability to communicate technically (2c).

Prepared by: Martin Corless

Date: March 1, 2001