Recent years have witnessed an enormous growth of interest in dynamic systems that are characterized by a mixture of both continuous and discrete dynamics. Such systems are commonly found in engineering practice and are referred to as hybrid or switching systems. The widespread application of such systems is motivated by ever-increasing performance requirements, and by the fact that high-performance control systems can be realized by switching between relatively simple LTI systems. However, the potential gain of switched systems is offset by the fact that the switching action introduces behavior in the overall system that is not present in any of the composite subsystems. For example, it can be easily shown that switching between stable subsystems may lead to instability or chaotic behavior of the overall system, or that switching between unstable subsystems may result in a stable overall system. In this book, we closely examine two classes of systems: switched systems (SS) and time-delay systems (TDS), which will eventually pave the way toward studying a new class of systems, switched time-delay systems (STDS).
KeywordsLyapunov Function Phase Portrait Functional Differential Equation Piecewise Linear Function Piecewise Linear System
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