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2.9 Advanced Stability Results 83
Figure 2.9.1: Input-output description of nonlinear system
as a Lyapunov function candidate.
The passivity of nonlinear systems was defined as follows [Narendra and
Taylor 1973], [Ortega et al. 1998].
DEFINITION 2.9–1 Consider the system shown in Figure 2.9.1 and assume
that it has the same number of inputs and outputs i.e. u(t) and y(t) have the
same dimension.
1. Passivity: The system is said to be passive if
for all finite T>0 and some γ>-∞.
2. Strict Passivity: The system is said to be strictly passive if there exists a
δ>0 and γ>-∞ such that
for all finite T>0.
EXAMPLE 2.9–1: Passivity of Rigid Robots
Consider again the robot equation
Copyright © 2004 by Marcel Dekker, Inc.
