Sampled-Data Stochastic Stabilization of Markovian Jump Systems via an Optimizing Mode-Separation Method

Abstract

This article addresses the stochastic stabilization problem of Markovian jump systems (MJSs) closed by a sampled-data controller in the diffusion part. A novel stochastic stabilizing method is developed by optimizing the mode separations whose quantity is equal to a Stirling number of the second kind. It can be used to deal with the challenges coming from a stochastic controller’s switching and state signals sampled, whose results are also less conservative compared to some existing results. In order to get the best mode separation having the best performance, an optimization problem is proposed by applying an augmented Lagrangian cost function, which can ensure the existence and calculability of a locally optimal solution. Moreover, an improved hill-climbing algorithm is established to reduce computational complexity while retaining as much performance as possible, which is enhanced by applying Q-learning technique to determine an optimal attenuation coefficient. Two examples are offered so as to verify the effectiveness and superiority of the methods given in this study.