Less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation

Abstract

This paper proposes less conservative stabilization conditions for Markovian jump systems with incomplete knowledge of transition probabilities and input saturation. The transition rates associated with the transition probabilities are expressed in terms of three properties, which do not require the lower and upper bounds of the transition rates, differently from other approaches in the literature. The resulting conditions are converted into the second-order matrix polynomial of the unknown transition rates. The polynomial can be represented as quadratic form of vectorized identity matrices scaled by one and the unknown transition rates. And then, the LMI conditions are obtained from the quadratic form. Also, an optimization problem is formulated to find the largest estimate of the domain of attraction in mean square sense of the closed-loop systems. Finally, two numerical examples are provided to illustrate the effectiveness of the derived stabilization conditions. Copyright (c) 2016 John Wiley & Sons, Ltd.