Geometric Theory of Nonlinear Systems: Applications
In this Chapter we show how the concepts introduced and developed in Chapter 6 can be effectively used in the solution of a number of important synthesis problems. We begin by considering the problem of local asymptotic stabilization at a certain equilibrium point. Our purpose is to extend the results developed in section 4.4, by showing that if the zero dynamics of a system are asymptotically stable at this point, the system itself can be locally asymptotically stabilized via state feedback. Of course, as stressed at the beginning of that section, our results are of special relevance only in case the linear approximation of the system is not stabilizable.
KeywordsVector Field Nonlinear System Closed Loop System Static Feedback Invariant Manifold
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