# CDS 101/110 - Linear Systems

## Overview

**Monday:** Linear Time-Invariant Systems (Slides, MP3)

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 introduced.

- Lecture handout
- MATLAB code: L4_1_linsys.m

**Wednesday:** Linear Systems Analysis (Notes, MP3)

Further analysis of linear systems, including a derivation of the convolution integral and the use of Jordan form. This lecture also covers the use of linearization to approximate the dynamics of a nonlinear system by a linear system.

- Lecture notes

**Friday:** recitations

## Reading

- K. J. Åström and R. M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, Preprint, 2006. Chapter 5 - Linear Systems.

## 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 Lypunov functions for linear systems and derivation of discrete time linear systems response functions.

- Homework #4
- balance_simple.mdl - SIMULINK model of a balance system
- ambode.m - Bode plot with AM unit choices

## FAQ

**Monday**
<ncl>CDS 101/110 FAQ - Lecture 4-1, Fall 2007</ncl>
**Wednesday**
<ncl>CDS 101/110 FAQ - Lecture 4-2, Fall 2007</ncl>
**Friday**
<ncl>CDS 101/110 FAQ - Lecture 4-3, Fall 2007</ncl>
**Homework**
<ncl>CDS 101/110 FAQ - Homework 4, Fall 2007</ncl>