Reachable Set Estimation For Discrete-time Interval Type-2 Fuzzy Systems With Time-delays

Due to the interval type-2 fuzzy model can be used to deal with the uncertain parameters of the nonlinear system,it brings challenges to the analysis and control of interval type-2 fuzzy systems.Reachable set analysis and estimation is one of important index for systems keeps safety and the automatic verification of safety.By utilizing effective analysis and synthesis methods.In this dissertation,the problem of reachable set analysis and estimation is studied for discrete time interval type-2 linear delay systems,discrete time interval type-2 bilinear delay systems and discrete time interval type-2 singular delay systems,respectively.The main contents are as follows:In the first part,the problem of reachable set analysis and estimation for a class of complex nonlinear systems with time delay and external input disturbance is discussed.In the first part,the problem of reachable set analysis and estimation is studied for a class of nonlinear system with both time delays and external disturbance.Firstly,the nonlinear system can be modeled by the discrete-time interval type-2 fuzzy model.Secondly,by constructing a set of appropriate Lyapunov-krasovskii functional,combining the properties of interval type-2 fuzzy sets in the proof process,and use matrix inequalities to define the intersection terms to obtain the sufficient conditions for the reachable sets with less conservatism.The condition of the theorem guarantees that all states of the system converge in an ellipse.Finally,the validity and correctness of the findings are verified by numerical examples and simulation results.In the second part,the estimation of reachable sets and the problem of dissipation for a class of discrete-time interval type-2 fuzzy bilinear systems with delay and external input perturbation are studied.Firstly,considering the parameter uncertainties in nonlinear system,the nonlinear system is modeled into the discrete-time interval type-2fuzzy bilinear delay systems.Secondly,by constructing Lyapunov-krasovskii functional,an discrete-time interval type-2 fuzzy state-feedback control criterion is proposed,and a sufficient delay-dependent less conservative dissipative stable condition of reachable set estimation is obtained for discrete-time interval type-2 fuzzy bilinear closed-loop systems via the reciprocally convex combination approach.The fuzzy controller can be obtained by using sequential linear programming matrix method.Finally,the validity and correctness of the findings are verified by numerical examples and simulation results.In the third part,the estimation of reachable sets and the problem of dissipation for a class of discrete-time interval type-2 fuzzy singular systems with delay and external input perturbation are studied.Firstly,considering the parameter uncertainties in nonlinear system,the nonlinear system is modeled into the discrete-time interval type-2fuzzy singular delay systems.Secondly,by constructing Lyapunov-krasovskii functional,and by using the matrix inequalities to bound the crossing terms,and a sufficient delay-dependent less conservative dissipative stable condition of reachable set estimation is obtained for discrete-time interval type-2 fuzzy singular closed-loop systems.Finally,the effectiveness and the correctness of the results are illustrated by three numerical examples.