Week 4: Linear Systems
Overview
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.
Reading Material and Handouts
Handouts from lecture
- Monday lecture handout
- MATLAB files: L4_1_linsys.m, lin2.m
- Homework #4
Required reading
-
K. J. Åström and R. M. Murray, Analysis and Design of Feedback Systems, Preprint, 2003. Chapter 4. (Caltech access only).
Supplemental reading
- Packard, Poola and Horowitz, Dynamic Systems and Feedback, Sections 19, 20, 22
Homework Set #4
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 the linearized model for the Caltech ducted fan.
- Homework Assignment
- MATLAB functions: (none)
- SIMULINK models: hw4cartpend.mdl