Research On The Stability For The Discrete-time Fuzzy Control Systems Based On The Takagi-Sugeno Model

As an active research field,the fuzzy control theory makes a rapid progress recently,which plays an important role in control fields.Fuzzy logic control is successfully applied to many control problems,such as pattern recognition,signal processing,machine intelligence,decision making,finance,medicine,and so on,because they do not need accurate mathematical models of the system and can cooperate with human experts' knowledge.The T-S fuzzy model is very important in the fuzzy control theory.Based on the model,the controlled system can be solved as differential equation.It is well known that the stability analysis is very important in system control and should be considered firstly.Due to the importance,it has drawn a large number of researchers' attention to study the problem.Based on the published results,this thesis gives more relaxed stability conditions by developing new Lyapunov function and controller which are constructed by a kind of matrix function.further more,it can deal with robust H_∞output feedback control problem effectively.First,the basis-dependent matrix function is developed by some definitions.Using the matrix function,a new Lyapunov function is obtained and some stabilization conditions are proposed by applying the Lyapunov function.It is proved that the new condition are equivalent to the previous ones,however,since the new conditions contain less variables and LMIs than the previous ones,it needs less computational time than before.The final simulation shows the effect of the new condition.It is worth pointing out that introducing slack variables is a useful and popular technique to reduce the conservatism of the obtained theorems.For discrete-time fuzzy system,the slack variables in the latest result are only introduced for the current time membership function,while in this thesis the slack variables are introduced for the current time membership function and next time membership function respectively and thus leading to less conservative results.For the continuous-time fuzzy system,new controller can be designed to reduce the conservatism. Further more,the relationship between the new result and the previous ones are discussed.Some examples are shown that the new theorems are less conservative than the published ones.Introducing slack variables for the current time membership function and next time membership function respectively do can reduce the conservatism of the obtained theorem,however, the computational burden increases too.In order to reduce the conservatism of the of the obtained theorem,at the same time,decrease the computational burden,a new method-increasing the degree of the matrix function instead of introducing exterior variables is developed.It is shown that the conservatism of the obtained theorems is reduced as the degree of the matrix function increases,although the number of the variables and LMIs increases,each linear matrix inequality is simple and easy to be solved and hence,the computational burden is reduced.Applying the method to deal with the state feedback H_∞control problem,the controlled system can be stabilized with the parameter varying in a larger area,in addition,the controlled system has good H_∞performance.The simulations show this point.At some time,there may be uncertainties in the system,some disturbance and some states of the system are unknown which needs observer to be observed.By applying the matrix function,new observer which contains previous ones as special cases,based on the observer the new H_∞controller are constructed to deal with this kind of system and new robustness H_∞stabilization conditions are obtained.The simulations show the proposed method is effective.