Exponential Mean‐Square Stability of Stochastic String Hybrid Systems Under Continuous Non‐Gaussian Excitation

Abstract

The problem of the exponential mean-square stability for nonlinear stochastic string hybrid system under parametric (multiplicative) Gaussian and external (additive) continuous non-Gaussian excitations is considered. The string hybrid system is treated as an infinite-dimensional family of strings (subsystems) with a switching rule that has the form of a right continuous Markov chain. It is described by infinite-dimension Ito stochastic differential equations. The excitations are assumed to be parametric Gaussian white noises and the continuous non-Gaussian processes modeled by polynomials of a Gaussian process. The nonlinear strings under external continuous non-Gaussian excitation are transformed to extended dimensional nonlinear strings with a special structure under a parametric Gaussian excitation. Using the methodology of the stability analysis of nonlinear hybrid systems with Markovian switchings the sufficient conditions of the exponential mean-square stability of nonlinear stochastic string systems under parametric Gaussian and external continuous non-Gaussian excitation with a Markovian switching are derived. The detailed calculations are given for linear systems.

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