H_∞ Control And H_∞ Filtering For Singularly Perturted Systems With Time Delay

In practice,most systems have time-delay phenomena in dynamic and control links,and singularly perturbed systems are no exception.Therefore,it is very meaningful to discuss the two cases.Therefore,the model of singularly perturbed systems with time delay can describe a wider class of systems.In addition,H∞ control meets the requirements of modern control theory for control stability,adaptability and intelligence.As the dual problem of control problem,the filtering of dynamic systems is the core problem of theoretical and practical significance in the field of control and signal processing.Therefore,the study of H∞ control and H∞ filtering for time-delay singularly perturbed systems has great theoretical significance and application prospects.In recent years,although the H∞ controller and the H∞ filter are studied by many scholars,the research results of singularly perturbed systems with time delay are still few.Therefore,in this paper,a H∞ controller and a H∞ filter are designed for a class of singularly perturbed systems with time-varying delay.The main research works are as follows:1.For a class of uncertain singularly perturbed systems with time-varying delay,a delay dependent robust H∞ controller design method is proposed.Firstly,the conditions of delayindependent and delay-dependent stability of the systems without control input are considered.For the problem of state feedback control with memory,based on the conditions that the state of the systems satisfying the bounded time-varying delay and the uncertainty satisfying the normbounded,the stability of the closed-loop systems and the sufficient conditions for the existence of the state feedback controller satisfying the performance of H∞ are studied by using the linear matrix inequalities method and Lyapunov stability theory.The sufficient conditions that do not depend on the perturbation parameter are obtained,which effectively avoid the ill-conditioned problems of numerical calculation.At the same time,the design method of the state feedback controller and the calculation method of the upper bound of the perturbation parameter under the given H∞ performance index are given.The results show that the delay-dependent state feedback controller can make the closed-loop systems meet the given performance requirement and reduce the influence of the delay on the systems.Finally,the effectivenes’s of the conclusion is proved by MATLAB simulation.2.For a class of singularly perturbed systems with time-varying delay,a delay-dependent robust H∞ filter design method is proposed.Firstly,the control systems to be studied is described and the filter is designed.By using the linear matrix inequalities method and Lyapunov stability theory,the sufficient conditions for the existence of robust H∞ filter are obtained to ensure that the filtering error systems are asymptotically stable and meet the given H∞ performance index.In order to verify the asymptotic stability of the filtering error systems,two delay-dependent sufficient conditions are given.One of which is to fully consider the influence of the perturbation parameter,and the other is to consider that the perturbation parameter may cause the ill-conditioned problems of numerical calculation,so a sufficient condition that does not depend on the perturbation parameter is proposed.An effective algorithm for the parameter upper bound to make the filtering error systems asymptotically stable is given.Finally,a simulation example is used to illustrate the effectiveness of our method.3.Based on the design method of robust H∞ filter for singularly perturbed systems with time-varying delay,the corresponding design method of robust H∞ filter is obtained for a class of uncertain singularly perturbed systems with time-varying delay.Finally,a simulation example is used to illustrate the effectiveness of the conclusion.