Analysis And Synthesis For T-S Fuzzy Systems Based On Delta Operator

In practical systems, nonlinearity possesses the property of dynamics systems, such as chemical processes, communication system, power system and biological system, etc. At the same time, the extraneous disturbances, the system parametric perturbations, the system failures and faults from external environment, will impact the internal stability and performance characteristics of the systems. As one of the factors impacting the stability and performance of the systems, time delay is frequently an important cause of instability and performance deterioration of the systems, which brings difficulty to the analysis and synthesis of the systems. In addition, with the rapid development of information technology, the high speed sampling system has been gradually drawn attention to. For discrete-time systems, the traditional displacement operator will lead to some difficulties when high-speed sampling period is used. For such case, the delta operator method is a new discretization method, especially proper for high-speed sampling systems. With a certain condition, the delta operator can be applied to a unified framework for continuous-time and discrete-time systems. For the class of discrete-time nonlinear systems with time delay based on delta operator, this thesis mainly concerns with the following content.A class of time nonlinear delay systems with uncertain extraneous disturbances is formulated based on delta operator. The T-S fuzzy model is applied to describing the nonlinear system. For different control and filtering objectives, fuzzy controllers(state-feedback-based one and the output-feedback-based one) and filters are established according to the parallel distributed compensation principle, which result in closed-loop control systems and closed-loop systems. Importantly, by using the small scale gain theorem, the time-varying delays embedded in the closed-loop systems are reconstructed via an input-output approach, and furthermore, a new type of the transformation model is established. Based on the model, new criteria of the stability for the closed-loop systems are derived by applying Lyapunov stability theory and the linear matrix inequality technique. To further detailed discussion, for this class of systems, the passive control scheme, dynamic output feedback control scheme, output tracking control scheme, output error filtering and fault detection schemes are presented in the thesis. For the validation of the effectiveness and practicability from the schemes, different simulation examples are provided and procedural in each chapter. Overall, with regard to the discrete-time nonlinear systems with time-varying delay and external disturbance, this thesis provides the basis and reference of the theory and methods for extended research and further application.