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36 Introduction to Control Theory
(2.3.8)
where U(k) and c are defined similarly to those given in equation (2.3.4).
EXAMPLE 2.3–3: Logistics Equation
Consider the scalar system
which leads to the state-space representation
We will not emphasize the study of discrete nonlinear systems since robots
are described by differential equations. However, as discussed in Chapter 4,
robot controllers are usually implemented using digital controllers. It will
therefore be advantageous to be able to translate between continuous-and
discrete-time description of nonlinear dynamical systems as discussed in
[åAström and Wittenmark 1995], [Franklin et al. 1997].
2.4 Nonlinear Systems and Equilibrium Points
In this section, we concentrate on systems described by (2.2.15) with the
additional requirement that u(t) is specified as a function of the state x(t),
i.e.
(2.4.1)
This will allow us to concentrate on the Analysis problem. We require a
few definitions which we shall now introduce.
Copyright © 2004 by Marcel Dekker, Inc.
