Output Feedback Robust Control Of Uncertain Switched Linear Discrete Time Systems With Multi-delays

Recently, the research of switched systems has made much progress. Due to the existence of the uncertainties and time delays in the real systems, the robust analysis and control for the switched systems with parametric uncertainties and time delays is becoming a hot research topic in the theories and applications. Since the states of the real systems are difficultly observed, the output feedback robust control of the uncertain switched systems with time delays has important theoretical and practical value.Based on the piecewise quadratic Lyapunov functions, Linear Matrix Inequality (LMI) and the cone complementarity linearization (CCL) algorithm, this dissertation investigates the robust stabilization, the non-fragile guaranteed cost control, the non-fragile H∞control and the output feedback controller design methods for the switched discrete-time systems with polytopic uncertainties and multi-delays. The main contributions are as follows:(1) Under the arbitrary switching signals, the observer-based output feedback robust stabilization is studied for the switched discrete-time systems with polytopic uncertainties and multi-delays. The synthesis method of the output feedback controllers is proposed based on the piecewise Lyapunov functions and state variable replacement method.(2) The non-fragile robust guaranteed cost output feedback control problem is investigated for the switched discrete-time systems with polytopic uncertainties and multi-delays. By applying the piecewise quadratic Lyapunov functions and CCL algorithm, the synthesis method that considers the controller gains perturbation is developed for the observer-based output feedback robust guaranteed cost control laws under the arbitrary switching signals.(3) For the switched discrete-time systems with polytopic uncertainties and multi-delays, the output feedback non-fragile robust H∞control problem is considered. The sufficient conditions are derived for guaranteeing the system asymptotical stability and the H∞disturbance attenuation level under the arbitrary switching signals. The design approach of the control laws is proposed for the output feedback non-fragile robust H∞control.