On Problems Of Robust Control For Delta Operator Switched Systems

The delta operator method is a discretization method of continuous-time systems.In the case of fast sampling,its discretization model can approach the original continuous-time systems model,and has better numerical properties.Switching system theory and application is a popular direction in the study of control theory.A switched system is a hybrid dynamic system composed of a series of continuous or discrete subsystems and the switching rules that coordinate these subsystems.The switching rules determine which certain subsystem is activated.When it is enabled,the switched system’s performance is better than any of its subsystems under the appropriate switching rule.In recent years,the research on the delta operator switching systems has also achieved certain development.In this paper,several problems of robust control of delta operator switching systems are studied,and the main work is as follows.The problems of D-stability robust guaranteed cost control for delta operator switched systems are studied.For a class of delta operator switched systems with polytopic uncertainties,a state feedback controller is designed such that the closedloop delta operator switched system is D-stable and the value of the closed-loop cost are less than a given upper bound.The H∞ control problems of delta operator switched systems with state signal quantization are studied.For a class of delta operator switched systems with external perturbation,the controller and dynamic quantizer are designed.The dynamic parameters of the quantizer do not directly depend on the system matrix.The quantized closed-loop switched system can achieve the same H∞ performance index as the closed-loop switched system without quantization.The problems of output feedback stability control for delta operator switched systems with uncertain parameters are studied,a new linearization scheme and a more general linear matrix inequality condition are proposed by using Finsler lemma,a design method of observer-based controller is discussed.