Sliding Mode Controller Design For Stochastic Singular Markov Jump Systems

In this paper,we study the design problem of robust H∞ sliding mode controller for stochastic T-S fuzzy singular Markov jump system with time-varying delay,one-sided Lipschitz nonlinear stochastic singular Markov jump systems,and discrete one-sided nonlinear singular Markov jump systems with time-varying delay,respectively.The main research works are as follows:1.By considering a class of stochastic T-S fuzzy singular Markov jump systems with timevarying delay,a robust H∞ sliding mode controller design method is proposed.It is well known that the sliding mode control strategy has complete robustness to the matching uncertainties or nonlinear terms of the control systems and has great significance to practical applications.Firstly,the systems which will be studied is described and a more general fuzzy integral type sliding surface function is designed,and by using the weak infinitesimal operators,a delay-dependent sufficient condition is proposed such that the sliding mode dynamics are stochastically admissible with H∞ performance.Secondly,a sliding mode controller which guarantees reachability condition of state trajectories is designed.Finally,simulation examples are utilized to show the effectiveness of proposed method.2.By considering a class of stochastic singular Markov jump systems with one-sided Lipschitz nonlinearities,a finite-time sliding mode controller design method is proposed.The first is to design a suitable integral sliding surface function and a sliding mode controller which can guarantee state trajectories reach the sliding surface in finite time.The second is to design a suitable Lyapunov-Krasovskii functional,and some sufficient conditions related to one-sided Lipschitz condition are proposed such that the sliding mode dynamics are singular stochastic H∞ finite-time bounded.In addition,a generalized condition of one-sided Lipschitz constants in singular systems is proposed via LMIs.Finally,simulation examples are utilized to show the effectiveness of proposed method.3.By considering a class of discrete singular Markov jump systems with time-varying delay and one-sided Lipschitz nonlinearities,a robust H∞ sliding mode controller design method is proposed.Firstly,based on the control systems,a switching surface function which contains control gains is designed,then by designing suitable Lyapunov-Krasovskii functional and free weight matrices,a sufficient condition related to one-sided Lipschitz condition is proposed such that the sliding mode dynamics is stochastically admissible with H∞ performance.Secondly,a sliding mode controller which guarantees reachability and deduces chatting is designed.Finally,simulation examples are utilized to show the effectiveness of proposed method.