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

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.