Stability Analysis And Design For Nonlinear System With Time-delay Based On T-S Model

With the development of science and technology, practical engineering controlsystems tend to nonlinearity, uncertainty, incomplete of information and strongcoupling. It will be difficult for applying traditional linear system theory to propose aneffective control strategy for this system. In addition, the phenomenon of time-delayoften exists in most of dynamic systems. Time-delay is the source of poorperformance and also is the important factor of instability for dynamic systems.Aiming at these problems, the stability analysis and controller design of nonlinearconstant time-delay systems, nonlinear time-varying systems and nonlinear time-varying delay systems with parameter uncertainties are discussed by applyingTakagi-Sugeno (T-S) fuzzy model in this dissertation.In this dissertation, the research mainly includes the following aspects:(1) Based on T-S model, the stability of nonlinear systems with constanttime-delay is studied. Firstly, this kind of nonlinear systems with constant time-delayis given in form of T-S fuzzy time-delay systems. Secondly, in order to decomposeconstant time-delay of the systems, an adjusted parameter is introduced. Then a newdelay decomposition approach is proposed, which is called unequal delaydecompositon method. Based on Lyapunov stability theory, a new Lyapunov-Krasovskii (L-K) functional is constracted by using this method. Sufficient conditionsfor the systems are obtained via derivativing the L-K functional along the track ofsystem. Finally, several numerical examples and simulation are provided to show thatthe sufficient condition compared with some of existing literatures has the advantagesof less conservative, less decision variables and more computing effectiveness.(2) If time-delay is a time-varying one，the stability of nonlinear time-varyingdelay system is concerned. Firstly, this kind of nonlinear systems with time-varyingdelay is given in form of T-S fuzzy systems with time-varying delay. Secondly, thetime-varying delay of systems is randomly divided into two parts. A new L-Kfunctional is defined by using this method and a less conservative delay-dependentstability criterion with less decision variables and more computing effectiveness isformulated in form of Linear Matrix Inequalities (LMIs). Besides, in the process ofreasoning and demonstrating the criterion, there is no need to introduce redundantfree-weighting matrices variables. Finally, a numerical example and simulation isprovided to show the effectiveness of the proposed method. (3) The problem of delay-dependent robust stabilization condition for uncertaintnonlinear systems with time-varying delay is concerned on the basis of (2). Thissystem can be described as an uncertain T-S fuzzy system with time-varying delay.The technique proposed in (2) and the L-K functional defined in (2) are applied toderive the delay-dependent robust stabilization condition. A less conservativedelay-dependent robust stabilization condition is formulated in form of linear matrixinequalities. Besides, an iterative algorithm is given to solve the problem of nonlinearmatrix inequalities. Finally, a numerical example and simulation is provided to showthe effectiveness of the delay-dependent robust stabilization condition for parameteruncertainties nonlinear system with time-varying delay.