Research On Observer-Based Control Of Delta Operator Switched Systems

With the development of science and technology,switched systems,as a kind of important hybrid systems,has attracted more and more attention from the control field at home and abroad.Delta operator has better performance than traditional shift operator and has better numerical characteristics.The application of delta op-erator method in the field of high speed signal processing and control has attracted the attention of many scholars.The delta operator switched system is obtained by describing each subsystem of the switched systems with delta operator method.State feedback plays an important role in the engineering implementation of various control problems such as pole assignment,stabilization and tracking control.However,due to the actual system itself or the economic or technical limitations of measurement means,it is generally difficult to obtain all the information of the system state.So designing observer to reconstruct system state has important theoretical and practi-cal significance.This paper mainly studies various control problems of delta operator switched systems based on observer.The main contents of this thesis are given as follows:The observer-based output feedback reliable stabilization of delta operator switched systems is studied.A sufficient condition for asymptotic stability of a class of delta operator switched systems with actuator failures is given by using switched Lyapunov function method.Then the output feedback stabilization controller based on observer is designed by using Yang’s inequality and matrix decomposition method.Non-fragile robust guaranteed performance control for observer-based delta op-erator switched systems is studied.Under the assumption that the controller contains additive uncertainties,The observer-based non-fragile exponential stability conditions of delta operator switched systems are derived by means of the average dwell time technique,and are characterized by linear matrix inequalities.According to Lyapunov stability theory,the system performance is analyzed,and the conditions for the exis-tence of observer-based non-fragile robust guaranteed performance controller for delta operator switched systems are given.At the same time,the corresponding controller design method is given,so that the cost function of the closed-loop system does not exceed an upper bound.An observer-basedH_∞fault detection method for delta operator switched sys-tems is proposed.An observer-basedH_∞fault detector is constructed for the delta operator switched systems,and a weightedH_∞performance index is introduced to improve the disturbance robustness of the system residuals.The average dwell time method is used to design theH_∞fault detector.