In this chapter, we introduce the notion of control sets, which is basic for our study of nonlinear systems. Control sets are maximal subsets of the state space where complete controllability holds. Section 3.2 analyzes their basic properties and presents a number of illustrative examples. Section 3.3 describes the reachability order on control sets and discusses control sets that are maximal within a subset of the state space. This allows us to characterize common regions of attraction of control sets. In Section 3.4, we briefly discuss chain control sets based on a weaker controllability notion allowing for arbitrarily small jumps.
KeywordsInvariant Control Approximate Controllability Local Accessibility Multistability Region Chain Control
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