Almost sure convergence and stability analysis of hybrid partial differential systems under jump Markovian perturbations

In this work, the jump Markovian perturbations caused by the interactions a mong the states of a hybrid parabolic partial differential system are inves tigated in the context of vector Lyapunov functions and random partial diff erential inequalities. Sufficient conditions for almost-sure stability and convergence are developed utilizing a block comparison theorem. Moreover, a n effort has been made to characterize the effects of Markovian random pert urbations in stability of such systems. In fact, it has been shown that the Markovian random perturbations are indeed the stabilizing agents. In addit ion, an example is given to illustrate the significance of the presented re sults.