Fuzzy Absolute Stability Of Lurie Delay Control System

The absolute stability of Takagi-Sugeno (T-S) fuzzy Lurie control systems with time-delays is investigated in this dissertation. It is well known that there are many papers reported on the stability analysis and control design for T-S fuzzy systems with LMI. This thesis does a new extension to use absolute stability of Lurie control systems with time delays for T-S fuzzy systems. The main purpose is to obtain the absolute stability conditions for T-S fuzzy Lurie control systems in the form of LMIs. This thesis mainly includes the following four parts :1. The problem of the absolute stability of a new class of T-S fuzzy Lurie control systems with time-varying delay is discussed. Taking advantage of the Lyapunov-Kraso vskii functional (LKF) , linear matrix inequality (LMI) and novel techniques, a new absolute stability condition is derived.2. We are to study the problem of the absolute stability of a new class of T-S fuzzy Lurie control systems with multiple time-delays. On the basis of the Lyapunov stability theory and the linear matrix inequality (LMI) approach, a novel delay-dependent absolutely stable condition is obtained. Finally, a simulation example is given to demonstrate effectiveness of the main result.3. The problem of the absolute stability of a new class of T-S fuzzy Lurie control systems with time-delay and time-variant uncertainties in the state as well as the nonlinearity functions is investigated. Based on Lyapunov-Krasovskii functional (LKF) together with linear matrix inequality (LMI) approach, a novel delay-dependent absolute stability criterion is derived. Meanwhile, we provide a simulation example to demonstrate feasibility and effectiveness of the proposed result.4. We contribute to the problem of the absolute stability of a new class of T-S fuzzy Lurie control systems with time-delay in the state and a new class of T-S fuzzy Lurie control systems with time-delay and nonlinearities. By means of novel techniques, new Lyapunov functions are constructed to achieve a new delay-dependent absolute stability criterion for each system. In the end, two numerical example and their simulation results are presented respectively to illustrate feasibility and effectiveness of the proposed results.