Control Design For Interval Type-2 Stochastic Fuzzy Systems

Type-1 Tagaki-Sugeno(T-S)fuzzy model is a common and powerful tool in the field of the approximation and description for complex nonlinear systems,and it has many applications in the actual production and life.Nevertheless type-1 fuzzy sets have limitations in dealing with uncertainties of fuzzy rules directly.The type-2 fuzzy sets of the type-2fuzzy system make it up for this shortcoming,and it can handle this issue of uncertainties.Because the operation of the type-2 fuzzy sets is more complex,its main application is in the interval type-2 sets.In this thesis,the stability analysis and controller design for the interval type-2 T-S model based It (?) stochastic fuzzy logic system are investigated.The primary results include the following three parts.The first part is considered with the controller design problem for the interval type-2uncertain It (?) stochastic fuzzy systems driven by a multidimensional Wiener process.By employing a stochastic Lyapunov function approach and inequality techniques,sufficient conditions for stochastic stability of the close-loop systems are established,and the approach of controller design is given.The form of the stability results is farther simplified via introducing the Kronecker product.A matrix decomposition technique is effective in dealing with parameter uncertainties and stochastic perturbations.Finally,the effectiveness of the proposed approach is illustrated via a simulation example.In the second part,we deal with stochastic stability problem for the interval type-2It (?) stochastic fuzzy systems with time-varying delays and unmatched premises.Because interval type-2 fuzzy basis functions and stochastic perturbations as well as time-varying delays are involved in,the complexity of stabilization problem increase,and it is more challenging to research.A delay-dependent Lyapunov-Krasovskii functional approach combined with delay decomposition technique is proposed to analyse the delayed It (?) stochastic interval type-2 fuzzy systems.A estimate of the Lie derivative of the LyapunovKrasovskii functional can be achieved by employing generalized It (?) isometry as well as using reciprocally convex combination which can be facilitated by a new function matrix decomposition skill.Based on this estimate,a less conservative stochastically stable in mean square condition is thus established for the underlying systems.Finally,the feasibility of the proposed approach is also illustrated by a simulation example.The third part focuses on the problem of the controller design for the interval type-2It (?) stochastic fuzzy systems with time-varying delays and unmatched premises.Based on the second part results,less conservative results of stability for the interval type-2stochastic fuzzy systems with time-varying delays are established,and the method of the control design is obtained by matrix variable transformation.According to known matrices,the value of the upper bound of time-varying delay can be obtained,and we can see that for the same lower bound of time-varying delay and the upper bound of the derivative of time-varying delay,the more number of the divide lower bound,the larger value of the upper bound.Finally,the effectiveness of the proposed algorithm is verified via a Monte Carlo simulation.