Improved ℋ∞ state-feedback control for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities(ICCAS 2015)

This paper considers improved ℋ_∞ state-feedback control for discrete-time Markovian jump systems with incomplete knowledge of transition probabilities. To achieve the better ℋ_∞ performance, this paper proposes two valuable approaches. First, under the assumption that the lower and upper bounds of unknown transition probabilities are known, the closed-loop stabilization conditions are represented as convex combination with these bounds. Second, a new lower bound lemma for the inversion of the matrix summation is investigated. This lemma enables the inversion of the matrix summation to be replaced by free variable which does not contain the transition probabilities. Thus, the ℋ_∞ stabilization conditions consist of two parts which are transition probability independent part and dependent part. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.