H_∞Filter Design For Complex Nonlinear Systems Based On T-S Fuzzy Model

Complex nonlinear system itself is a relatively broad concept, which encompassesthe nonlinear interconnected system, nonlinear switched systems, nonlinear networksystems, and so on. However, we only study of nonlinear switched systems, nonlinearinterconnected system in this paper.Switched systems are an important class of hybrid system which containscontinuous dynamic and discrete dynamic. Furthermore, switched systems can bedescribed as a group of subsystems and a switching signal to control the switchingbetween them. In real life, such systems have a large number of applications in theautomotive industry, the control of mechanical systems, aircraft and the control of airtraffic, switching power converters and many other fields. The difficulties of suchsystems are the switching characteristics and strong nonlinear of the systems. Althoughit is usually considered that the switching rule is arbitrary in the switched system, asuitable switching signal is critical in improving the system performance. Currently,some special switching signals are under study, such as the hysteresis switching, dwelltime (average dwell) time switching and so on. However, up to now, to our knowledge,the average dwell time switching is still recognized as a more efficient and flexibleswitching signal in the stability analysis of switched systems.In addition, system theory faces a major challenge is the real-world physics,engineering and social systems, such as power systems, nuclear reaction system, spaceflight systems, economic systems, which are increasingly high-dimensional complexinterconnected systems. The difficulties of these interconnected systems are thelarge-scale properties of the system and strong nonlinearity. Prior to this, the researchersused the Lyapunov theory and the T-S fuzzy model so that many control problems ofsuch systems have been effectively discussed. Filtering problem is the dual problem ofsystem control, and it is the theoretical basis and engineering guidance of signalestimation and output feedback control. Predecessors have been some studies aboutfilter designing of discrete-time fuzzy interconnected systems with delay. Unfortunately,there is hardly a viable solution in the filtering problem of continuous-time fuzzy interconnected system with delay.Therefore, the research in this paper is as follows1) For the discrete-time nonlinear switched system, based on Lyapunov theory andT-S fuzzy model, using the piecewise Lyapunov function method, I have analyzed theH_∞filtering problem with exponential stability.2) For the discrete-time nonlinear switched system with time-varying delay, basedon delay-dependent piecewise fuzzy Lyapunov functional, I have designed theexponentially stable H_∞filter. Sufficient condition for exponential stability of filtererror system is transformed into a series of linear inequalities. Then, we can design afuzzy filter for discrete-time switched nonlinear systems with time-varying delay.3) For continuous-time nonlinear interconnected system with time-varying delay,based on delay-dependent fuzzy Lyapunov functional and T-S fuzzy model, using freeweight matrix method and the decentralized design approach, I have analyzed the H_∞filtering problem. Then, we can design a fuzzy filter for continuous-time nonlinearinterconnected system with time-varying delay.4) In order to prove the effectiveness of the filtering, I have simulated someinstances with MATLAB.