Week 4: Input/Output Behavior
Overview
Monday: This lecture gives an introduction to linear input/output systems. The main properties of linear systems are given and the matrix exponential is used to provide a formula for the output response given an initial condition and input signal. Linearization of nonlinear systems as an approximation of the dynamics is also covered.
Wednesday: Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form.
Friday: Prof. Steven Low (CS/EE) will give a lecture on computer networking and control. The lecture will explain how congestoin is controlled on the Internet, described the major protocols, and their mathematical models, and analyze their behavior around equilibrium using linear systems analysis.Handouts
Monday (CDS 101/110)
- Monday lecture handout
- MATLAB files: L4_1_linsys.m, lin2.m
- Homework Set #4
Wednesday (CDS 110 only)
Reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2004. Chapter 4 . (Caltech access only).
- Packard, Poola and Horowitz, Dynamic Systems and Feedback, Sections 19, 20, 22
Homework
This homework set covers linear control systems. The first problem asks for stability, step and frequency response for some common examples of linear systems. The second problem considers stabilization of an inverted pendulum on a cart, using the local linaerization. The remaining problems (for CDS 110 students) include derivation of discrete time linear systems response functions and derivation of a linearized model for internet congestion. Supplemental problems for flight control and robotics are available.
- HW #4
- SIMULINK models: hw4cartpend.mdl
Additional Information