| Most of physical systems and industrial processes are described by nonlinearmodels. Traditional linear control theory is helpless in those new areas. Comparedwith the well developed linear control, fruits about nonlinear control theory are rel-atively less, especially those that can applied to solve practical problems. In recentyears, the Takagi-Sugeno(T-S) fuzzy model, which is described by a family of fuzzyIF-THEN rules, has become an effective measure to investigate the nonlinear sys-tems. In fact, those rules in the T-S fuzzy model represent the local linearization ofa nonlinear model. So, by the T-S fuzzy model, the original nonlinear system can betransformed into a group of linear systems under the fuzzy rules. In this measure, thewell-developed linear control theory can then be applied to solve the original nonlinearcontrol problems. On the other hand, time-delay commonly exists in many practicalcontrol systems, especially those related with chemical industry and communicationengineering. The existence of time-delay generally lowers system performance andeven induces oscillation and instability. Therefore investigation of time-delay systemsis necessary. In addition, in some practical systems, stochastic noise is an unavoidablefactor. In the cases of high-precision control requirement, the influence of stochas-tic noise cannot be neglected. Due to its special feature in frequency domain, thestochastic noise cannot be thoroughly eliminated by filtering. Then the systems withstochastic noise must be treated as stochastic systems.Stability is the basic requirement for any control systems, and without it systemscannot work properly. Dissipativity describes the input-output property of systemsfrom the energy point of view, and it also provides a new concept for the analysisand design of control systems. For the discrete-time T-S fuzzy stochastic systems, itsstability and dissipativity analysis are generally conducted by the Lyapunov method.Great effort has been made to reduce the conservativeness and complexity of obtainedresults. Based on the existing method, in this paper, we will adapt new methodsto settle the delayed state in systems, and then investigate stability, dissipativity andcorresponding synthesis problems of discrete-time T-S fuzzy stochastic systems. Thespecific work can be illustrated as:Firstly, for the discrete-time T-S fuzzy stochastic systems with time-delay, delay-partitioning method is applied to evenly partition the lower bound of time-varying delay. Delay-dependent and basis-dependent Lyapunov-Krasovskii functional is thenconstructed based on the states at partitioning moments. Also combined with someslack matrices, the obtained result will have lower conservativeness. Finally, thedelay-dependent stability condition is transformed into strict linear matrix inequali-ties.Secondly, a two-term approximation method is applied to approximated thetime-varying delayed state. Then a novel model transformation method is introducedto pull the time-varying delay uncertainty out of the original system. Consequently thetransformed model is composed of a linear time-invariant system and a norm-boundeduncertain subsystem. Based on the former simplification, a new Lyapunov-Krasovskiifunctional is constructed to obtain the dissipativity results. Finally, all results are con-verted into linear matrix inequalities which can be solved by computer.Thirdly, the related synthesis problems of discrete-time T-S fuzzy stochastic sys-tem are investigated based on the former stability and dissipativity analysis. By anon-parallel distributed compensation strategy, available fuzzy controller is designedto ensure that, the closed-loop systems satisfy required stability, dissipativity and H∞criteria.Fourthly, based on the obtained system synthesis method, some special controlproblems of three class of practical systems (namely, stabilization problem of a in-verted pendulum on a cart, the dissipative control problem of a model car, the optimalH_∞control problem of the EMS system) are investigated. |
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