Page 77 -
P. 77
58 Introduction to Control Theory
Figure 2.6.8: Example 2.6.2 (a)time history; (b) phase plane
centered at x e and given by such that
both stability and asymptotic stability will result for any state starting in
but not for states starting outside of it. This region is called the
domain of attraction of x e. The equilibrium state x e is GAS if .
Note also that all previous stability definitions depended on the initial
time t 0, so that the region of attraction may vary with varying initial times. If
the system (2.6.1) were independent of time (or autonomous), then the
stability concepts in definition 2.6.1 are indeed independent of t 0 and they
Copyright © 2004 by Marcel Dekker, Inc.
