Finite-time Stochastic Stabilization via Output Feedback Controller for Networked Control Systems with Markovian Jump Systems Approach

This paper deals with the problem of finite-time stochastic stability and stabilization of networked control systems in the presence of random delay. At first, the network random delay is modeled as a Markov chain, and the resulting closed-loop system is a Markovian jump linear system. Since, due to network complexities, the accurate access to transition probabilities are hard or even impossible, some of the elements in the transition probability matrix are considered as unknown. Then, according to the definition of finite-time stochastic stability for discrete-time Markovian jump systems, a sufficient condition is proposed to guaranty the boundedness of the system states in the sense of mean-square, in a determined time interval. In the next step, the results are extended for the finite-time stochastic stabilization problem of this specific class of systems and the output feedback controller is designed such that the closed-loop system is stochastically finite-time stable. All the results are presented in the form of new linear matrix inequalities (LMIs). The main contribution of this paper is utilizing the static output feedback controller for finite-time stochastic stabilization of the closed-loop system; besides, new LMIs are employed to calculate the output feedback control law. Also, in order to verify the theoretical results and show the applicability of the proposed controller, simulations are performed for two systems.