Analysis And Design For T-S Model Based Stochastic Nonlinear Systems

This thesis considers the problems of stability analysis and controller synthesis for a class of T-Smodel based nonlinear stochastic systems. The considered systems contain time-delay, random noise,parameter uncertainty, Wiener process and the external random disturbances. T-S fuzzy modeling is awell-established and convenient tool for handling complex nonlinear systems based on the stochasticLyapunov stability theory. The primary results obtained in this paper include the following three parts.The first part is concerned with the stability analysis problem for a class of stochastic fuzzy de-lay systems with Gaussian white noise by using delay decomposition approach. Lyapunov-Krasovskiifunctional is constructed by uniformly dividing the delay interval into multiple segments and choos-ing proper functional with different weighted matrices for each segment. New delay-dependent con-ditions are derived such that the system is asymptotic stability in the mean square sense based on Ito?formula. It is shown that the result obtained with this approach is less conservative than some otherexisting results. And a numerical example given also demonstrates the effectiveness and merits of theproposed method.In the second part, we discussed the stabilization problem of a class of uncertain Ito? stochasticfuzzy systems driven by a multidimensional Wiener process. The objective is to design a state-feedback fuzzy controller such that the closed-loop system is robustly asymptotically stable undera stochastic setting. The uncertainty modeled in the systems is of the linear fractional type whichcan describe a class of rational nonlinearities and includes the norm-bounded uncertainty as a specialcase. Because of the linear fractional nature of the uncertainty description and the involvement of amultidimensional Wiener process, the problem considered is technically challenging as it cannot bedirectly dealt with by the previous robust techniques proposed by others. A new matrix decompositionmethod has to be introduced so as to make the previous technique applicable. The main contributionof this part is that sufficiency conditions of robust stochastic stability and stabilization are derived forthe systems considered by using a novel matrix decomposition technique and stochastic Lyapunovapproach. Based on these conditions obtained, a desired controller can be designed to guarantee thestability of the closed-loop systems. Monte Carlo simulations are given to illustrate the effectivenessof the approaches proposed.In the third part, the issues of H_∞control are investigated for a class of T-S model baseddiscrete stochastic systems with or without uncertainty. There are two types of disturbances in thesystems, such as stochastic noises and external random disturbances. Both the state and externalunknown disturbances are dependent on the stochastic noises. The results on stability analysis are given based on the robust control theory to make sure that the systems considered are stochasticallyasymptotically stable and the H_∞performance are satisfied. Then, a state-feedback fuzzy controllercan be designed by using the principle of Parallel Distributed Compensation. Sufficient conditionsfor the solvability of the H_∞control problem are established. Finally, numerical examples areprovided to demonstrate the effectiveness of the results obtained.