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2.4 Nonlinear Systems and Equilibrium Points 37

DEFINITION 2.4–1 The system (2.4.1) is said to be autonomous if f[t, x(t)]
is not explicitly dependent on time, i.e.

(1)

EXAMPLE 2.4–1: Nonautonomous System
Both systems introduced in Example 2.3.1 are autonomous while the system
described by

is not.

n
DEFINITION 2.4–2 A vector x e ∈ is a fixed or equilibrium point of (2.4.1)
at time t 0 if

(1)

EXAMPLE 2.4–2: Equilibrium Point of Autonomous System
The system described by

is autonomous and it has an equilibrium point at the origin of .
n

Note that:

• If a system is autonomous, then an equilibrium point at time t 0 is also an
equilibrium point at all other times.

Copyright © 2004 by Marcel Dekker, Inc.