Nam Kyu Kwon, Bum Yong Park, PooGyeon Park
Optimal Control Applications and Methods
Abstract This paper proposes less conservative stabilization conditions for Markovian jump systems with incompleteknowledge of transition probabilities and input saturation. The transition rates associated with the transitionprobabilities are expressed in terms of three properties, which do not require the lower and upper bounds ofthe transition rates, differently from other approaches in the literature. The resulting conditions are convertedinto the second-order matrix polynomial of the unknown transition rates. The polynomial can be representedas 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?nd 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 ⓒ 2016 John Wiley & Sons, Ltd.