Necessary and sufficient conditions for analysis and synthesis of Markov jump systems with partially known transition rates

This paper addresses the analysis and synthesis problems for continuous-time Markov jump systems with partially known transition rates (TRs) when there is no extra assumption that the lower bounds of unknown diagonal elements in TR matrices are known. By fully considering the property of TRs and applying the method of reduction to absurdity, quadratic stochastic stability and stabilization criteria are obtained. The proposed criteria are both sufficient and necessary while in the existing literatures only sufficient criteria are reported in the means of quadratic stochastic stability.