Reliable Control For Delta Operator Systems With Time-delay

Delta operator is a new discretization method, using the method discrete time system become Delta operator system. In the certain conditions, the Delta operator system integrate continuous time system and discrete time system into a synthetic research framework.Along with developing of the Delta operator, its application study has been paid more and more great attention. In the actual engineering of control, the time-delay phenomenon commonly occurs in the industrial control system, such as communica-tion system, chemical process, metallurgical process, biological system, power sys-tem and so on. It often leads to systems instability and poor performance. Besides, there are other factors that cause instability and poor performance of systems, envi-ronmental factors and system components, for example. The problem of designing reliable controllers that can tolerate component failure of control system is so-called reliable control problem.In the paper, we mainly study the problems of reliable control for a class of delta operator formulated systems with time-delay and parameter uncertainties. The research is mainly focused on the following aspects:The problem of reliable guaranteed cost control for a class of delta operator formulated systems with time-delay and parameter uncertainties is studied. The aim is to design a state feedback controller which makes the close-loop systems robust asymptotically stable and the value of cost function less than a certain up-per bound for all admissible uncertainties and actuator failures. In the discussion, norm-bounded parameter uncertainties,convex polytopic uncertainties and actuator failures with continuous model are considered. Based on Lyapunov theory in delta domain, a sufficient condition of existence of the controllers is presented in terms of linear matrix inequalities. And then a design method of the controllers is proposed. A numerical example is given to illustrate the availability and effectiveness of the method.The problem of reliable stable control for a class of delta operator formulated systems with time-delay and parameter uncertainties is studied. The aim is to design a state feedback controller which makes the close-loop systems robust asymptotically stable for all admissible uncertainties and actuator failures. In the discussion, linear fractional parameter uncertainties and actuator failures with continuous model are considered. Based on Lyapunov theory in delta domain and LMI method, a sufficient condition of existence of the controllers is presented. And then a design method of the controllers is proposed. A numerical example is given to illustrate the availability and effectiveness of the method.The problem of reliable H∞control for a class of delta operator formulated systems with time-delay and parameter uncertainties is studied.The aim is to design a H∞controller which makes the close-loop systems robust asymptotically stable for all admissible uncertainties and actuator failures.In the discussion, norm-bounded parameter uncertainties and actuator failures with continuous model are consid-cred.Based on Lyapunov theory in delta domain, a sufficient condition of existence of the controllers is presented in terms of linear matrix inequalities. And then a de-sign method of the controllers is proposed. A numerical example is given to illustrate the availability and effectiveness of the method.