Analysis And Optimal Synthesis For Fuzzy Systems With Time Delays And Stochastic Perturbations

Most physical systems and processes are nonlinear in many areas of real world engi-neering, thus serious difculties are introduced in system analysis and design. In this case,the conventional powerful linear control theory is of little use. However, it is not easy tofind the solution to a general nonlinear system problem if not impossible at all, or the ob-tained results are too restrictive to be used. The advent of the Takagi-Sugeno (T-S) fuzzymodel suggests an efective method for the analysis and synthesis of nonlinear systems.It has been proved that T-S fuzzy models can approximate any smooth nonlinear systemto any accuracy on a compact set, and the parallel distributed compensation scheme isalso an approximation of nonlinear controllers. Based on obtained T-S fuzzy model, theproblem of filter design and model reduction can be solved for the concerned nonlinearsystems. On the other hand, transmission delay, data packet dropout and stochastic dis-turbance, which are the main sources of degraded systems’ performance, are inevitablyintroduced to the complex control system in rapid developmental of engineering applica-tions. It is noted that most present developments available focused on these phenomenain linear systems, and few systematic results have been reported for nonlinear systems.Many researchers have addressed delayed fuzzy systems with sensor fault, but there is stillmuch room to be developed further. Therefore, based on the T-S fuzzy models, this thesisaims to propose novel techniques on the analysis and synthesis of nonlinear systems withtransmission delay, data packet dropout and stochastic disturbance. Moreover, some ofthe presented theoretical results will be extended to application of fuzzy controller designfor nonlinear electromagnetic suspension systems. The above eforts set up a completeand systematic research framework and form the main line of investigation for "Analysisand Optimal Synthesis For Fuzzy Systems with Time Delays and Stochastic Perturba-tions". The main contents, novel techniques and original theoretical contributions of thisthesis are presented as follows:1. Chapter2proposes some novel methods combined with the construction of basis-dependent Lyapunov function, the delay partitioning method, the input-outputmethod and the reciprocally convex method, to solve the stability analysis prob-lem of discrete-time T-S fuzzy time-varying delay systems, and obtains the delay-dependent conditions with further less conservativeness. Then, based on the ob- tained less conservative stability results, Chapter3is focused on the problemsof H_∞output feedback control for T-S fuzzy time-varying delay systems, andHankel-norm output feedback control for T-S fuzzy stochastic systems. Combin-ing the delay partitioning method with the input-output method, the output con-troller is designed by the construction of the basis-dependent Lyapunov functionfor T-S fuzzy systems with time delays and stochastic perturbations, which makesthe corresponding closed-loop system stable with the given performance.2. Chapter4is concerned with the system performance analysis and filter designfor T-S fuzzy systems with time-varying delay and stochastic disturbance. Suf-ficient conditions of stability analysis satisfying the given performance level arepresented for the augmented error system by the delay divisioning approach incombination with the input-output approach. Based on these conditions, the fil-tering problem of T-S fuzzy systems with time-varying delay is solved efciently.Furthermore, the obtained conditions are extended to solve the problem of H_∞filter design for T-S fuzzy systems with time-varying delay and stochastic distur-bance. All of these filtering conditions are in terms of a set of strict linear matrixinequalities and are obtained by employing the basis-dependent Lyapunov func-tional technique and the convex linearization technique.3. Based on the proposed filtering results of T-S fuzzy systems with time-varyingdelay and stochastic disturbance in Chapter4, the reliable filtering problem is s-tudied for T-S fuzzy delayed systems with incomplete sensor information first.Based on the extension of reciprocally convex idea to the construction of basis-dependent Lyapunov function, the desired reliable filter for T-S fuzzy systemswith time-varying delay is obtained, which makes the corresponding error systemstable with strict dissipativity. Then, considering the occurrence of incompleteinformation in sensor network, the distributed filtering problem of T-S fuzzy sys-tems with time-varying delay is settled by introducing the topological structureand scale small gain theorem in sensor network. Finally, the distributed filter withaverage H_∞performance constraint is designed in terms of the feasibility of aconvex optimization problem.4. Chapter6first investigates the problem of model reduction for high-order T-Sfuzzy stochastic systems. Based on the existing results on mean-square stabili-ty analysis with H_∞performance level, two diferent solutions of reduced-order model parameters are given by the convex linearization and projection lemma, re-spectively. Then, the model reduction problem for high-order T-S fuzzy stochasticsystems is further extended to high-order T-S fuzzy switched stochastic systems,which are subject to several modes of T-S fuzzy stochastic systems. By con-structing the piecewise parameter-dependent Lyapunov function, the mean-squareexponential stability condition with Hankel-norm performance index is presentedfor T-S fuzzy switched stochastic systems. Based on this index, the Hankel-normmodel approximation method for T-S fuzzy switched stochastic systems is ob-tained in the form of linear matrix inequalities.5. Chapter7first gives the fuzzy modelling process of a magnetic levitation mod-ule in electromagnetic suspension system, which is represented as a4-rules’ T-Sfuzzy model. According to the technique in solving fuzzy control problems of T-Sfuzzy systems in Chapter3, a fuzzy state feedback controller is designed guar-anteeing the electromagnetic suspension system to be operated safely. The simu-lation results of the electromagnetic suspension system show the efectiveness ofthe proposed fuzzy state feedback controller. The obtained results of this chapteris the extension of the fuzzy controller design based on the T-S fuzzy system andprovide a fuzzy control design example for electromagnetic suspension system topractical engineers’ reference as well.