Asian Journal of Mathematics and Computer Research

The problem of the stability of a class of stochastic linear hybrid systems under parametric non– Gaussian continuous excitation with a special structure of matrices is considered. The input process is modeled as a polynomial of a Gaussian process. The linear systems under a parametric non– Gaussian continuous excitation are transformed to extended dimensional linear systems with a special structure under a parametric Gaussian excitation. Using the methodology of the stability analysis of linear hybrid systems with Markovian switchings and any switchings the sufficient conditions of the exponential p-th mean stability and the almost sure stability for a class of stochastic linear hybrid systems under parametric non–Gaussian excitation with a Markovian switching and the mean–square stability for a class of stochastic linear hybrid systems satisfying Lee- algebra conditions under parametric non–Gaussian excitation with any switching are derived, respectively. The obtained stability criteria are illustrated by two examples and simulations.