Stochastic stability robustness and H 2 performance robustness of continuous-time Markovian jump linear systems with uncertain transition rates via μ analysis

Abstract

This paper considers the stability robustness and H 2 performance robustness of continuous-time Markovian jump linear systems with uncertain transition rates. Based on the Kronecker product, the robustness problems are transformed into problems of judging whether a class of uncertain matrices can maintain nonsingularity. For the robust stability problem, the method for computing the robust upper and lower bounds of transition rates is given first and then the necessary and sufficient condition for the investigated system to maintain robust stochastic stability is given when considering interval uncertainty. For the robust H 2 performance problem, the robustness bounds and sufficient and necessary conditions guaranteeing the robust H 2 performance are similarly given. The robustness bounds for analysing the tolerance of continuous-time Markovian jump linear systems to parameter uncertainties can be conveniently computed by utilising the proposed results. Numerical examples illustrate that the results are less conservative than existing results.