Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump

This paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely unknown. Based on calculating the weak infinitesimal generator and combining Poincare inequality and Green formula, a stochastic stability criterion is given in terms of a set of linear matrix inequalities (LMIs) by the Schur complement lemma. Because of the existence of the neutral term, we need to construct Lyapunov functionals showing more complexity to handle the cross terms involving the Laplace operator. Finally, a numerical example is provided to support the validity of the mathematical results.