Research On Robust Fuzzy Control And Filtering For Nonlinear Time-Delay Systems Via LMI Approach

Control and filtering of nonlinear time-delay systems are important issues of control theory. Based on Takagi-Sugeno (T-S) fuzzy model and linear matrix inequality (LMI) method, the dissertation investigates the problems of robust fuzzy control and fuzzy filtering, which mainly covers the following six aspects:(1) Delay-dependent stability analysis and synthesis of continuous-time delay T-S fuzzy systems are thoroughly studied. By constructing Lyapunov-Krasovskii functions that take more consideration of the interrelationship of various factors in system state functions, the dissertation proposes a new delay-dependent stability criterion via LMI approach. The delay-dependent criterion, compared with existing ones, has lower conservation, and relaxes the restriction to time-delays of the control systems. On the basis of this, sufficient conditions are presented for the existence of the delay-dependent fuzzy controller described by nonlinear matrix inequality (NMI). Considering the difficulty to solve NMI, the dissertation also proposes direct LMI algorithm and improved particle swarm optimization-LMI (IPSO-LMI) hybrid algorithm. IPSO-LMI hybrid algorithm transforms the solution procedure of NMI into an evolving optimization procedure, which takes the control performance as its target. It is proved by examples that IPSO-LMI algorithm can be used to design controllers with superior performance, which provides useful instruction for other similar NMI problems.(2) The dissertation extends the delay-dependent synthesis methods used in nominal systems to continuous fuzzy time-delay systems with time-varying uncertainties and proposes a design method for delay-dependent H_∞ fuzzy state feedback controllers. Under immeasurable situation of system states, the dissertation introduces a PI style fuzzy output feedback control method. It retains the simple structure of traditional static output feedback controllers, while improves the design flexibility and results in better control performance. The delay independent and delay dependent methods are used respectively in this work to establish sufficient conditions of the existence of PI fuzzy output feedback controller and their design schemes.(3) Delay-dependent stability criteria and robust stabilization controller design schemes for uncertain discrete-time T-S fuzzy delay systems are proposed. First, a new discrete Lyapunov function is constructed. Observing the different methods to solve Lyapunov function differential equation and based on LMI technique, two delay dependent stability criteria are introduced with difference in their formation but equal in essence. Then, with the results of stability analysis, the dissertation derives two designing strategies for delay dependent fuzzy controllers, which have their own characteristics in controller parameters design. The effectiveness of these methods is illustrated by numerical examples.(4) Applies the principles in designing non-fragile controllers to the decentralized fuzzy guaranteed-cost control and decentralized H=° fuzzy control issues of uncertain nonlinear time-delay large scale interconnected systems. By Lyapunov stability theory, the dissertation gives the control law to the stability of closed-loop T-S fuzzy large-scale interconnected delay systems with additive and multiplicative perturbation. The designing of non-fragile controllers subject to certain control performance requirement can be finally concluded to the solution of LMIs.(5) Based on T-S models, the energy-to-peak fuzzy filtering problem of nonlinear stochastic time-delay systems is studied. With respect to continuous-time and discrete-time T-S fuzzy stochastic time-delay systems, under the definition of stochastic stability, the dissertation proposes LMI-based systematic designing scheme for robust fuzzy filter, which guarantees the filtering error dynamic systems satisfy a prescribed L2-L0* (for continuous-time systems) or /2-/o°(for discrete-time systems) noise attenuation level for all energy-bound noise signals.(6) Taking permanent-magnet synchronous motor in chaos as a controlled object, this thesis examines the application of robust fuzzy control methods in networked control systems. The simulated experiments on Matlab6.5 prove its validation.