STOCHASTIC HYBRID PARABOLIC SYSTEMS UNDER JUMP MARKOVIAN PERTURBATIONS-I: CONVERGENCE AND STABILITY VIA LYAPUNOV FUNCTIONALS

摘要

In this paper, we investigate convergence and stability concepts in the sense of p-th mean and probability of the solution process of stochastic parabolic systems under Markovian structural perturbations. Sufficient conditions are obtained for various kinds of convergence and stability. This is achieved by developing a powerful comparison theorem in the context of vector Lyapunov-like functionals and systems of differential inequalities. The class of jump linear systems (JLS) was introduced by Krasovskii and Lidskii in the early sixties. Since then we have seen an increasing interest in this class of systems. It has been applied to model various dynamical systems, such as manufacturing systems, socio-economic systems, etc. For more information regarding the application of such systems, we refer the reader to Mariton, Sethi and Zhang and the references therein.