Control And Synthesis Of Discrete Switching Systems Based On Dwell Probability Information

Switched systems are a kind of hybrid systems which are composed of a set of continuous or discrete subsystems and the switching rule.The switching rule coordinates these subsystems.Among them,switching rules can also be called switching laws,switching functions or switching signals,which determine how the subsystems can be switched.Therefore,the stability of the switching system depends not only on the subsystems,but also the switching rules.It is more complex and challenging for the research of switched systems because of the introduction of the switching rules.Numerous practical engineering applications can be represented by switching systems,such as switching of power system networks,multi-point switching of aircraft or automobiles,and control of multi-frequency sampling digital systems.It is helpful to solve the above engineering application problems through the research of switched systems,which is of great significance both in theory and practice.This paper introduces a new type of switching rules--random switching rules based on the sojourn probability information,in which the sojourn probability refers to the probability that the system stays in a particular subsystem for enough time.Based on the method of sojourn probability information,a set of random variables are introduced to reconstruct the discrete switching systems,thus a new set of random systems are obtained.Based on the newly established discrete random systems,the output feedback control of the switched system is studied by using the Lyapunov functional method and linear matrix inequality technique.On this basis,the observer based state estimation problem of the discrete time switched system and the cost control problem are studied.Then by considering the saturation factor in the actual system,the problem of H? control for uncertain discrete systems with actuator saturation is analyzed.Firstly,by using sojourn probability,a new kind of switched system model is given for a class of discrete time switched systems.Sufficient conditions for the robust H? stability of such systems are presented by using Lyapunov functional method and linear matrix inequality technique.The H? performance level y and robust output feedback gains and observer gains are also obtained.Then the effectiveness of the proposed method is verified by a simulation example.Secondly,this paper studies the guaranteed cost control problem of a class of discrete time-delay switched systems with parameter uncertainties.A new switched system model is constructed by using the sojourn probability information,which does not depend on the system state or switching sequence.Meanwhile,the cost functional is established.Then the sufficient conditions for quadratic stability of the system are obtained by solving a set of specific linear matrix inequalities.Considering the uncertainties of the system parameters,the sufficient conditions for the existence of guaranteed cost controllers are derived under the linear matrix inequality method.The simulation results show that the proposed method can satisfy the desired performance of the system.Finally,considering the time delay,uncertain factors and the actuator saturation in partial switched system,a new model of switched systems using means of sojourn probability information is established.Furthermore,the sufficient conditions for the robust H? stochastic stability of the switched system and the H? performance level y of the system are obtained.Then the attraction domain of the actuator saturation estimation system is expanded.At last,the effectiveness of the proposed method is verified by a numerical example.