Sliding-Mode Variable Structure Control For Markov Jumping Uncertain Systems With Time-Varying Delay

One of the most important hybrid systems is the so-called Markov Jumping System (MJS), in which the mode-process taking values in a finite set. In engineering applications, MJS can be represented by different forms depending on the value of an associated Markov chain process. Time-delay and uncertain parameter are often encountered in various engineering systems, such as turbojet engines, electrical networks, and so on. The existence of time-delay and uncertain parameter is frequently a source of instability and poor performance. A famous technique is called the sliding-mode variable structure control (SM-VSC), which is designed to drive and constrain the system states to lie on a neighbourhood of the prescribed switching manifolds that exhibits desired dynamics. Hence, this paper considers the SM-VSC problem for Markov jumping uncertain systems with time-delay. The main results obtained in this thesis are as follows:1. For a class of Markov jumping uncertain systems with time-varying delay, by studying nonsingular transform of the system and using the linear matrix inequality (LMI) approach, a sufficient condition for the existence of stochastic stable sliding surfaces is established depending on the time-varying delay bounds and uncertainties. On the basis of this existing condition, the synthesized SM-VSC algorithm is designed via exponential approach law, which is proved to guarantee that the system trajectory reach the sliding surface in finite time and keep up here thereafter. Finally, an illustrative example demonstrates the correctness and feasibility of the proposed algorithm.2. In order to deal with the uncertainties and time-varying delay, the sufficient conditions of the stochastic stable sliding surface are proposed respectively based on LMI, and that is designed to stabilize the sliding motion with H∞disturbance attenuation level y Furthermore, the SM-VSC algorithm is designed to drive the state of the MJS to reach the sliding surface in finite time and remains on it thereafter. Finally, a numerical example is given to illustrate the correctness and feasibility of the proposed algorithm.3. The SM-VSC algorithm is proposed for a class of Markov jumping nonlinear systems via Takagi-Sugeno (T-S) model. First, the Markov jumping model with uncertainties and exterior disturbance is derived by employing T-S model to represent original system. Then the control problem becomes the robust stabilization controller design for uncertain MJS. By using the LMI technique, a sufficient condition for the existence of stochastic stable sliding surface is established. On the basis of this existence condition, the synthesized variable structure control approach is designed, which is proved to guarantee that the system trajectory reaches the sliding surface in a finite time interval and keeps up here thereafter. Finally, a numerical example is given to demonstrate the correctness and effectiveness of the proposed algorithm.Finally, the summarization of the research work in this paper and the potential research directions are pointed out.