Analysis And Control For T- Fuzzy Singular System With Time-delay

Takagi-Sugeno(T-S) fuzzy singular models can approximate any nonlinear singular system in any small error, and fuzzy controller via parallel distributed compensation strat-egy is also approximation of a global controller, which can make use of fruitful results on linear singular system control field to solve complex nonlinear singular systems possi-ble. The research of T-S fuzzy singular systems has been received much attention. Some results of theory and application have been made, but there is still much room and open problem for improvement. A further study should be made to obtain more effective con-ditions for admissability analysis and controller designing with less conservatism. Based on T-S fuzzy singular model with time-delay and stochastic disturbance, and by use of Lyapunov theory, this thesis aims to propose novel ideal and techniques on the analysis and synthesis and explore its potentials of nonlinear singular systems. Moreover, some of the obtained theoretical results will be applied to fuzzy singular control for the complex nonlinear stotch yoke mechanism. The main work and original theoretical contributions of this thesis are summarized as follows:The problems of admissibility analysis for T-S fuzzy singular with interval time-varying delay systems are investigated. By taking into account the structure of time-varying delay, by employing an appropriate Lyapunov-Krasovskii functional, by applying and free weighting matrices and Jensen’s inequality, two novel conditions are proposed by combining fuzzy basis dependent methods with delay partitioning method and the reciprocally convex approach. All obtained conditions are in terms of LMI and it can be can be extended to the general form that the lower bound of time delay is zero. Compared with existing methods, it shows that the results obtained in this chapter with more freedom and further less conservativeness.The problems of dissipativity analysis and controller design for T-S fuzzy singular with constant time-delay are studied。 Obtained results are extended to the analysis and synthesis problems for passivity and H∞ performance. By employing delay partition-ing method and slack matrices technique, a novel condition is given to make the system be admissible and strict (Q,R,S)-α dissipative. All obtained conditions are dependent on time-delay and dissipativity index α. Furthermore, delay dependent condition for the existence of the problem of stabilization, and effective designed processing for desired controller are given. Meanwhile, conditions on analysis and corresponding design meth-ods of desired controllers for passivity and H∞ performance are given in the form of extended corollary. Numerical examples are given to show the effectiveness and the less conservatism of the presented methods.The problems of admissibility analysis, passivity analysis and passification for T-S fuzzy singular with time-delay and stochastic disturbance are concerned with. Firstly, based on an appropriate Lyapunov-Krasovskii and Ito formula and combined free weight-ing matrix technique with novel inequality method, the sufficient condition is given in the form of strict LMI, which shows the system is stochastically admissible and passive. As an extension, the case of nonlinear density function meeting Lipschitz condition is addressed. Furthermore, delay-dependent criterion for the solvability for the problem of state feedback controllers and effective design methods for the desired state-feedback controller are presented by two different procedures. Among them, cone complementar-ity linearization method is used to solve non-convex constraints during controller design process, and given the corresponding algorithm. Simulation examples demonstrate the effectiveness of the theory obtained in this section.The problems of sliding mode control for T-S fuzzy singular with parameters uncer-tainty and nonlinear disturbance are discussed. Firstly, the proof of a key lemma is given. A sliding mode surface of integration type is specified related with derivative matrix and fuzzy basis. Then, we construct an appropriate Lyapunov-Krasovskii function by using of delay partitioning methods and deserve sufficient condition that make the nominal of sliding mode system to be admissible by employing lemma and free weighting matrices technique. And, the uncertain case of sliding mode system is considered. Next, sliding mode law is designed to meet the performance constraints. When some parameters can-not be measured, adaptive sliding mode law is also given. The simulation results show that the system is able to reach the designed sliding surface in finite time and meets the desired performance requirements, which verifies the validity of the obtained results in this chapter.The problems of robust admissibility and non-fragile guaranteed cost control are ad-dressed for uncertainty T-S fuzzy singular time-delay system with controller gain pertur-bations. A cost function is given associated with the system state and input. An appropri- ate Lyapunov-Krasovskii function is constructed by taking account into an upper bound of time-delay. Under a unified framework, sufficient condition is proposed with additive and multiplicative disturbances, which meets the performance requirements. Two type of con-trollers are designed for different controller gain perturbations that makes the closed-loop systems meet the constrained quadratic functions. Least upper bound of cost function is obtained through optimization technique. Meanwhile, to be compared with the previous results, an admissible condition is obtained in the form of corollary. Finally, simulation examples are given to validate the effectiveness and superiority of the obtained results.Some part of theoretical results are used to control a scotch yoke mechanism sys-tem. The fuzzy modeling process of a scotch yoke mechanism is given, which is repre-sented as a 8-rules’T-S fuzzy singular model. According to the technique in fuzzy-basis-dependent of T-S fuzzy singular systems in Chapter 2, a fuzzy state feedback controller is designed guaranteeing the scotch yoke system to be operated safely. Based on the actual physical parameters, the simulation results of the scotch yoke system system show the effectiveness of the proposed fuzzy state feedback controller. The obtained results of this chapter is the extension of the fuzzy controller design based on the T-S fuzzy singular system and provide a fuzzy control design example for scotch yoke mechanism system to practical engineers’s reference as well.