ℋ∞ state-feedback control for continuous-time Markovian jump systems with partly unknown transition probabilities(ICCAS 2015)

This paper considers the ℋ_∞ state-feedback control for continuous-time Markovian jump systems with partly unknown transition probabilities. The aim of this paper is to derive the ℋ_∞ stabilization condition such that the MJS with partly unknown transition probabilities is stochastically stable with γ-disturbance attenuation. First of all, the transition rates associated with the transition probabilities are expressed in terms of the three properties without the lower and upper bounds of the transition rates, differently from other approaches in the literature. Then, with consideration of the properties of transition rates, the ℋ_∞ stabilization conditions are derived in the quadratic form. And then the quadratic form can be replaced by the linear matrix inequalities(LMIs). Finally, a numerical example is presented to illustrate the effectiveness of the proposed method.