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2.2 Linear State-Variable Systems 25

Figure 2.2.1: (a) State-space block diagram of (2.2.6); (b) Transfer function block
diagram of (2.2.6)

EXAMPLE 2.2–1: Double Integrator
Consider a SISO system described by

ÿ(t)=u(t)

This system is known as the double integrator and represents a wide variety
of physical systems described by Newton’s Law. In order to obtain a state-
space description, let

so

Copyright © 2004 by Marcel Dekker, Inc.