This chapter discusses invariance principles, which characterize the sets to which precompact solutions to a dynamical system must converge. They rely on invariance properties of ω-limit sets of solutions, and additionally on Lyapunov-like functions, which do not increase along solutions, or output functions. Invariance principles which rely on Lyapunov-like functions are first presented, and their applications to the analysis of asymptotic stability are then described. The chapter next states an invariance principle involving not a Lyapunov-like function, but an output function having a certain property not along all solutions, but only along the solution whose behavior is being analyzed. Finally, the chapter presents invariance principles for switching systems with dwell-time switching signals modeled as hybrid systems.
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