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32 Introduction to Control Theory

(2.3.2)

The output equation then reduces to:
y(t)=x 1(t) (2.3.3)

A more compact formulation of (2.3.2) and (2.3.3) is given by

(2.3.4)

where

(1)
U(t)=[u(t) u (t)…u (n-1) (t)] T

and

c=[1 0 0…0]. (2.3.5)

EXAMPLE 2.3–1: Nonlinear Systems
We present 2 examples illustrating such concepts:
1. Consider the damped pendulum equation

A state-space description is obtained by choosing x 1=y, x 2=y, leading to

The time history of y(t) is shown in Figure 2.3.1.

Copyright © 2004 by Marcel Dekker, Inc.