Controlling And Filtering For Time-Delay Systems With Incomplete Information

Time delays frequently appear in many practical systems such as power systems and signal transmission.The existence of delays often results in instability or poor performances.Hence,the stability analysis of systems with time delays has been one of the hottest issues in control field.What's more,the signal will be affected by the external disturbance during the transmission,which leads to the deviation of the received measured signal from the real signal.To reduce this deviation,people usually apply the filtering method to filter the signal.Filtering(State estimation)is defined as the process of using certain filtering methods to estimate the signal that cannot be measured in the system or restore the real signal that is interfered by noise based on the measurement output.The H? filter,as one of the important filtering methods,introduces the H? norm indicator in the design process and its ultimate goal is to design an effective filter satisfying the criterion that the norm of output from the disturbance input to the filter error is less than a certain value,correspondingly,a stable filter is designed by using the measured signal to estimate the state of the system.This paper considers the filtering problem of time-delay systems with incomplete information,and the main research contents of this paper are as follows:(1).The stability and H? performance of interval time-varying delay systems is investigated.The aim is to find new optimal analysis method,which can integrate the constructed Lyapunov-Krasovskii functional(LKF)with estimating technique effectively to reduce the conservatism of the main results.A new augmented vector and LKF with triple integral terms are constructed to establish relationships among different vectors firstly.Then two different integral inequalities are used to show how to integrate constructed LKF with estimating technique effectively to reduce the conservatism of the main criteria.Meanwhile,less conservative criteria are derived compared with some existing results;(2).H? state estimation of neural networks with mixed delays is considered.In order to make full use of delay information,novel delay-product-type Lyapunov-Krasovskii functional(LKF)by using parameterized delay interval is firstly constructed.Then,generalized free-weighting-matrix integral inequality is used to estimate the derivative of LKF to reduce the conservatism.Also,a more general activation function method is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model.Finally,sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed H? performance;(3).The issue of H? state estimation of static neural networks(SNN)with randomly occurring controller gain fluctuation is concerned.The extended Luenberger-type observer is firstly established to estimate the SNNs with time-varying delays and more general.In order to make full use of time delay and derivative of time delay,some novel delay-product-type Lyapunov-Krasovskii functional(LKF)is firstly constructed.Then the Auxiliary function-based integral inequalities and the improved reciprocally convex inequality are utilized to estimate the derivative of LKF to reduce the conservatism.Finally,the main work of the paper is sum up,and the development of the analysis of controlling and filtering for time-delay systems with incomplete information is discussed.