Abstract
AbstractThis paper applies the spectrum technique to investigate the general stability of stochastic Markov jump linear systems (SMJLSs). First, the notion of spectrum for SMJLSs is defined and the relationship between the spectrum and the asymptotical mean square stability is revealed. Second, by analyzing the spectrum distribution in the complex plane, some new concepts of stability, such as critical stability, regional stability, and essential instability, are introduced for SMJLSs. Necessary and sufficient conditions on such general stability are established. Finally, several numerical examples are carried out to illustrate the developed theory.
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