Adaptive gain-scheduling control for uncertain Markovian jump systems. A transition rate synthesis method

This paper is concerned with the gain-scheduling control for a class of uncertain Markovian jump systems, in which the uncertainties are described via the polytopic representation. In order to reduce the conservatism brought from the common/parameter-independent control method in existing results, an adaptive gain-scheduling controller is designed whose gain is constructed as a convex sum of a fixed set of controller gains. Under the assumption of a given transition rate matrix, the controller gains and adaption laws of polytopic parameters are co-designed to ensure the stochastic stability of the resultant closed-loop system. Furthermore, taking the characteristic of Markovian transition rates, a co-designed scheme is developed to obtain controller gains, transition rate matrix, and adaption laws, simultaneously. Finally, a numerical example is adopted to illustrate the proposed method.