Static Output Feedback Sliding Mode Control For Time-delay Systems

Researches of time-delay systems and sliding mode control theory are introduced, and the research background and significance of this paper is indi-cated briefly. Based on Lyapunov stability theory, sliding mode control theory and the singular system theory, the static output feedback sliding mode control for time-delay systems with nonlinear terms and uncertain time-delay systems with nonlinear terms are discussed, the nonlinear terms satisfy a norm-bounded condition and the time-delay is constant. By using a singular system approach, the stability of sliding mode and the designing of the static output feedback controller are discussed. The following results are proposed:(1) In chapter2, the static output feedback sliding mode control for con-stant time-delay systems is discussed. First, the sliding mode and the lin-ear switching surface are treated as a singular time-delay system. Based on the stability theory of singular time-delay systems, constructing a Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) sufficient condition is proposed, which guarantees that the sliding mode is stable. Second, according to some matrix inequalities, an LMI sufficient condition is given such that the closed-loop system is asymptotically’stable, and a static output feedback slid-ing mode controller is designed. A norm restriction is proposed to ensure that the state trajectories of the closed-loop system are convergent to the switch-ing surface in finite time. Last, numerical examples are given to illustrate the effectiveness and correctness of the proposed methods. This part has been accepted as a paper by ACTA AUTOMATICA SINICA.(2) In chapter3, the static output feedback sliding mode control for uncer-tain time-delay systems is discussed. First, based on the method for nominal systems discussed in chapter2, an uncertain singular time-delay system can be constructed by the sliding mode and the linear switching surface. Then, an LMI sufficient condition is given to guarantee the robust stability of the sliding mode. Next, in terms of LMI, a sufficient condition which guarantees that the closed-loop system is robust asymptotically stable and a static out- put feedback sliding mode controller are obtained. A norm restriction which ensures that the state trajectories of the closed-loop system are convergent to the switching surface in finite time is proposed. Last, a numerical example is given to illustrate the effectiveness and correctness of the proposed methods.One innovation of this paper is that there is no decomposing of the systems and switching surface, the gain matrix of the switching surface is designed at a time according to the stability of the sliding mode. The conditions for stability of the sliding mode and asymptotically stability of the closed-loop systems are all indicated directly by the original system coefficient matrices and switching surface gain matrices. It can avoid the complicated numerical problem caused by decomposing the systems.Another innovation of this paper is that the conditions for stability of the sliding mode and asymptotically stability of the closed-loop systems are all strict LMI conditions, there are no equation constraints, and free matrices in LMI conditions can increase the degrees of freedom of the solution to get a better result.