Stability and stabilization of discrete systems with random and uncertain parameters

Abstract A class of time-varying and nonlinear discrete systems with random and uncertain parameters is considered. The method of an estimation (evaluation) of the probability or the certainty index that the system is globally asymptotically stable is presented. The estimation consists in the determination of the lower and upper bounds for the probability and the certainty index via the determination of a sufficient condition and a necessary condition for the global stability. A specific stabilization problem is formulated. A typical case with structured uncertainties is considered. Simple examples illustrate the presented approach.

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