The Control Problem Of Semi-Markov Jump TS Fuzzy System

Because the sojourn time of Markov jump systems(MJSs)obeys exponential distribution,the transition rate of the system is time-invariant.This feature brings some limitations to the application of Markov jump systems.However,the sojourn time of semi-Markov jump systems(S-MJSs)obeys non-exponential distribution,which has more extensive application value.On the other hand,T-S fuzzy logic theory has provided an attractive and effective method for the synthesis of complex nonlinear systems,which can approximate nonlinear systems with arbitrary accuracy.Based on this situation,this paper uses T-S fuzzy logic theory to study the quantized finite-time control and sliding mode control of semi-Markov jump systems.The main research contents are as follows:Firstly,the problems of quantized finite-time control is studied for nonlinear semi-Markov jump T-S fuzzy systems.In this paper,the input quantization based on finite time control of logarithmic quantizer is studied for the first time.To solve the problem of how to design a T-S fuzzy-model-based finite-time control law in the presence of quantized error,this paper uses Lyapunov function to analyze the performance of finite-time boundedness via establishing sojourn-time-dependent sufficient conditions within a given finite-time level.Then the results are further transformed into the standard form of linear matrix inequalities(LMIs),and the specific form of the quantization controller is given.Finally,an example for an electric circuit shows the effectiveness of the finite-time control scheme.Secondly,the problems of sliding mode control is addressed for semi-Markov jump T-S fuzzy systems with time delay.First of all,in order to reduce some conservativeness,an integral sliding mode surface is designed without assumption that the input matrices are plat-rule independent with full column rank.Then,based on Lyapunov functional theory,the sufficient condition is provided for stochastic stability of the closed-loop system,and extended to the case where the input matrices are independent of plant-rule.Next,a fuzzy sliding mode controller is established to guarantee the finite time reachability of the predetermined fuzzy manifold.Finally,the superiorities of the proposed method are validated by a single-link robot arm model.Thirdly,the issues of sliding mode control of It (?) stochastic fuzzy systems with semiMarkov process is concerned.First,by using a supplementary variable technique and a plant transformation method,phase-type semi-Markov jump systems can be equivalently expressed as its associated Markov jump systems.Then,an integral sliding surface is designed,and sufficient condition is provided for robustly stochastic stability of the closed-loop systems.In addition,a fuzzy sliding mode controller is synthesized to ensure that the associated Markov jump T-S fuzzy systems satisfy the reaching condition.Finally,numerical examples show the effectivenss of the conclusions.