State Estimation And Passivity Problems For Switched Time Delay Systems Based On An ADT Approach

Switched systems are an important class of hybrid systems, which have broad applications in engineering. Due to the interaction among the continuous-time (discrete-time) dynamics, discrete event states, the existence of time delays and stochastic phenomenon, the dynamic behavior of switched stochastic delay systems is complicated. Mechanis of system evolution is not clear and many problems of analysis and synthesis of such systems remain to be studied. Thus, it is both theoretical as well as practical value to investigate these problems. The main contributions are as follows.Due to the case that the state of systems is usually unmeasurable in actual engineering, the problem of observer design for switched delay recurrent neural networks is studied. The attention is focused on designing the full-order observers to guarantee the exponential stability of the error dynamic system. Based on the average dwell time (ADT) approach and the free-weighting matrix technique, delay-dependent sufficient conditions are developed for the solvability of such problem and formulated as linear matrix inequalities (LMIs). The error-state decay estimate is also given. Then, the stability analysis problem for the switched recurrent neural networks can be covered as a special case of our results.The problem of robust H∞filtering for a class of uncertain switched neutral system subject to stochastic disturbance and time-varying delay is studied. Attention is focused on the design of a full-order switched filter such that the filtering error system is robust mean-square exponentially stable with a prescribed weighted H∞performance. Based on the average dwell time approach and the piecewise Lyapunov function technique, sufficient conditions for the solvability of this problem are obtained in terms of LMIs.The problems of passivity and passification for continous and discrete time switched stochastic systems are studied. The passivity property is adopted to analyze the influence of the external disturbance on such systems for achieving attenuation levels. Based on average dwell time approach and free-weighting matrix method, delay-dependent sufficient conditions are obtained in terms of LMIs, which ensures switched stochastic delay system to be mean-square exponentially stable and stochastically passive. The state decay estimate is also given. Then, the switched passive controllers are synthesized by linearization techniques.