# Lecture 4.1: Linear Systems

#### 21 October 2002

 Lecture Reading FAQ Homework CDS 101

### Lecture

This lecture gives an introduction to linear control 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.

Mud card responses [advanced search]:

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## No matches found

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\n"; print \$footer; }

### Reading Material and Handouts

#### Handouts from lecture

The following materials were handed out in lecture. These have been updated to include any corrections.

### Homework Set #3

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.

Modifications to the homework (link above is always the latest version):

• 26 Oct 02: version 1.1 release
• Fixed small typo in problem 1a (see FAQ below)
• 21 Oct 02: problem set release

Frequently asked questions on homework and TA hints: