![]() ![]() The chapter describes the use of graphs to come up with a simple characterization of stabilizability. A review of the necessary theoretical background in electrochemistry and solid state chemistry is given in Chapters 2 through 5. For this reason, there has long been a concerted effort to delineate classes of decentralized systems that can always be stabilized by local (state or output) feedback. When the method fails, the outcome is inconclusive that is the case with most of Liapunov-type results. The chapter uses the method of vector Liapunov functions to confirm that a selected control law stabilizes the system. ![]() The nonexistence of structurally fixed modes is a relatively simple characterization of potentially successful decentralized control structures. This chapter discusses the concept for design-oriented results, which are useful in the decentralized control of complex systems using local state feedback. When a vector function establishes the stability of the overall system, the autonomy of each subsystem is preserved and, as expected, connective stability follows. The reason is that each component of a vector function can be used independently to show the stability of a locally controlled subsystem. A natural way to establish the connective stability of a complex system driven by decentralized control is to apply the Matrosov–Bellman concept of vector Liapunov functions. ![]()
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