Stability Analysis And Robust Control For Uncertain Time-delay Systems

Time-delay systems exist quite widely in industrial and engineering problems, such as communication systems, biological systems, chemical systems and electrical networks. The existence of delay makes the system analysis and synthesis become more complicated and difficult. Meanwhile, delay is frequently a source of instability and performance degradation in many dynamic systems. In addition,the uncertainty of the system describes the difference between the mathematic model and controlled plant, which reflects the existing of the variation of the system parameters and disturbance. Thus, it is of a great importance in theoretical and pratical application to study the robust control for the uncertain time-delay systems, and considerable attention has been paid to the research on the stability analysis and controller synthesis of the uncertain time-delay systems.Based on Lyapunov-Krasovskii functional method, this dissertation devotes on the design of feedback controller for uncertain time-delay systems by LMI. The main work of this dissertation are outlined as follows:1,The problems of state feedback and Memory and Memoryless Compound state feedback robust H_∞controller design for a class of nonlinear uncertain state delay systems are studied. Some delay-independent and delay-dependent sufficient contitions are given in the terms of linear matrix inequalities.2,The robust stabilization for a class of nonlinear uncertain neutral systems with multiple time delay is mainly discussed. Because the uncertainty of this class of system is bounded by a linear function of the norm of the delayed states with unknown bounds, an adaptive update law is proposed to estimate the square of these unknown bounds. An adaptive control law is thereafter constructed. It is proved by Lyapunov stability theory that the solution of the closed loop system is uniformly ultimately bounded.3,First, The problems of robust stabilization for a class of matched nonlinear uncertain neutral system with time-varying delay or constant delay are investigated. By applying the Lyapunov stability theorem, two adaptive sliding mode controller (ADSMC) are developed. Based on sliding mode control technique, the proposed controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the dynamics of system reach the sliding plane, the proposed controlled systems are insensitive to uncertainty. Finally, for a class of nonlinear uncertainty time-delay linear systems which do not satisfy the matching conditions, a new delay-dependent sliding mode control strategy is proposed based on Lyapunov stability theorem. The control strategy can guarantee the existence of the closed-loop system's sliding phase, furthermore,global stability of sliding motion on sliding surfaces is proved.4,The problem of fault-tolerance control against sensor failures in linear state feedback systems is considered for a class of uncertainty neutral delay systems by using linear matrix inequality(LMI) based on the Lyapunov stability theory. A sufficient condition for the systems to be asymptotically stable, which is dependent on whether LMI is feasible, is presented. By solving the linear matrix inequalities(LMIs), we can obtain the robust fault-tolerance controller.5,The problems concerning the design of output feedback controller based on new type observational state for a class of neutral delay systems are investigated and a staged designing scheme of the observer and controller is then presented. The output feedback controller,which is delay_independent,can be obtained by means of solving three linear matrix inequalities.6,The stability of a class of time-delay interconnected systems with input delay and parametric uncertainties is considered by using the so-called reduction method. Then, a feedback controller design technique for decentralized stabilization is provided. Unlike existing results, the controller utilizes the information on the delay and employs the feedback of the past control history as well as the current state; thus, the performance is improved and conservativeness is reduced significantly. With Lyapunov's direct method, a sufficient condition for the stability is derived in terms of linear matrix inequalities (LMIs). Hence, all results can be solved efficiently. Finally, a numerical example is provided to illustrate the proposed method.The most results of this dissertation are presented by means of LMIs. The key to this method is to express the control objectives, such as asymptotical stability, H_∞performance etc., by means of LMIs, and to express the parameters of controllers in terms of the solutions to LMIs. The results show that the effective methods to deal with the LMIs are the matrix transformation, similarity transformation and Schur's Complement Lemma. Simulation results are given at the end of each chapter for major design schemes. Simulation results show the effectiveness of the proposed approaches.