H ∞ control of a class of extended Markov jump linear systems

A class of extended continuous-time Markov jump linear systems is proposed in this study. The generality lies in that the discrete dynamics of the class of systems is described by a Markov stochastic process, but with only partially known transition probabilities, which relax the traditional assumption in Markov jump systems that all the transition probabilities must be known a priori. Moreover, in contrast with the uncertain transition probabilities studied recently, no structure (polytopic ones), bounds (norm-bounded ones) or ‘nominal’ terms (both) are required for the partially unknown elements in the transition rate matrix. The sufficient conditions for H∞ control are derived via the linear matrix inequality formulation such that the closed-loop system is stochastically stable and has a guaranteed H∞ noise-attenuation performance. A tradeoff can be built using our approach between the difficulties to obtain all the transition probabilities and the systems performance benefits. A numerical example is provided to show the validity and potential of the developed theoretical results.