Stability And Feedback Control For Delay Systems With Actuator/Controller Failures

Time delay phnomenon widely exists in many industrial processes. Also, the faults of components such as actuators, controllers, occur inevitably with the running of systems. These may result in instability and poor performance of the resulting systems and complicate stability analysis and synthesis of the control systems. Therefore, it is a challenge for us to study this class of systems.Different from the design of the original reliable control, the paper mainly focuses on stability and feedback control of time-delay systems with actuator/controller failures by introducing a switching strategy and utilizing the framwork of switched system. Due to the interaction among the continuous dynamics, discrete dynamics and time delays, the behavior of such systems is very complicated. Mechanism of system evolution is not clear and many problems of analysis and syntheses need to be studied. Here, some problems of stability and controller design of the resulting closed-loop systems caused by actuator/controllelr failures are considered by constructing the piecewise Lyapunov-Krasovskii functional and by applying methods such as the average dwell time technique, multiple Lyapunov function method, the integral inequality, free weighting matrices, a combination of descriptor model transformation approach and Moon's integral inequality and so on. The main contributions of this dissertation are as follows.The issue of robustly exponential stability for a class of multi-delay systems with structure uncertainties or/and nonlinear perturbations and controller failures, is considered. Multi-delay system with actuator failures is modelled as a special switched delay system including both stable and unstable subsystems. Based on the average dwell time concept and using the integral inequality and the piecewise Lyapunov-Krasovskii functional, it is proved theoretically that the given switched system is robustly exponentially stable with a desired stability margin by dividing the total activation time into the time with stable subsystems and the time with unstable subsystems, in the context that the average dwell time and the ratio of the activation time with stable subsystems to the activation time with unstable subsystems are not less than a specified constant. And the resullts are extended to the case with nonlinear perturbations.The sovable problem of state feedback controller for the delay systems with both structure uncertainties and nonlinear perturbations is considered. Utilizing the established robustly exponentially sufficient condition and using matrix transformation, the sovable condition is obtained by introducing new matrix varables. Similarly, by using Lyapunov-Krasovskii functional, the delay-range-dependent stability condition is given in terms of LMIs and the sovable condition of the uncertain system with interval time-varying delay is also obtained.The stability property for uncertain switched delay systems caused by actuator failures, which are composed of stable subsystems and unstable ones, is addressed. By using the average dwell time idea and the total activation time ratio between stable subsystems and unstable ones, it is shown theoretically that the resulting closed-loop system is robustly exponentially stable for an allowable upper bound of delays if its corresponding system with zero delay is exponentially stable. Particularly, the maximal allowable upper bound of delays can be obtained by solving some feasible linear matrix inequalities. Then, the design problem of hybrid dynamical output feedback controller for robustly exponential stabilization of a class of uncertain systems with time-varying delays and controller failures is investigated. By representing the time-delay system in the descriptor form and using the average dwell time technique, a new delay-dependent stabilization criterion for the existence of output feedback controllers is obtained in terms of matrix inequalities. A cone complementary linearization algorithm is utilized such that the resulting closed-loop switched systems are stable for the normal and/or faulty cases.The issue of exponential stabilization for a class of special time-varying delay switched systems resulting from actuator faults is considered. The time-varying delay is assumed to belong to an interval and can be slow or fast time-varying function. Based on the average dwell time method incorporating with free weighting matrices, a hybrid state feedback strategy is redesigned to guarantee the stability of the system. New delay-range-dependent stabilization conditions using state feedback controllers are formulated in terms of linear matrix inequalities by choosing appropriate Lyapunov-Krasovskii functional without neglecting some useful knowledge on system states. The obtained results are less conserva tive. Numerical examples are given to demonstrate the feasiblity and the effectiveness of the proposed method.The problems of delay-dependent robustly exponential stability and stabilization of a class of special neutral systems with interval time-varying delays and actuator failures, are investigated. For the special switched neutral system resulting from actuator failures, based on the switching strategy of average dwell time method and the integral inequality approach, the delay-dependent sufficient conditions for exponential stability and stabilization of the special switched neutral systems are established in terms of linear matrix inequalities by choosing appropriate piecewise Lyapunov-Krasovskii functional. Also, the stabilizing hybrid state-feedback controllers are designed to guarantee that the closed-loop system is robustly exponentially stable. Particularly, the stabilization of the switched delay systems are obtained.This paper concerns the observer-based adaptive control problem of uncertain time-delay systems with stuck actuator faults. The system model is expressed as a switched system. Under the case that the original controller cannot stabilize the faulty system, multiple adaptive controllers are designed and suitable switching logic is incorporated to ensure the closed-loop system stable and state tracking. New delay-independent sufficient conditions for asymptotic stability are obtained based on piecewise Lyapunov stability theory.