Research On Sliding Mode Control Problem Of Persistent Dwell-Time Switched Systems

In recent years,switched systems have received a lot of attention from both academic and engineering communities,and the main research motivation is that considering the influence of various factors,the structure and parameters of the system will exhibit switching characteristics,and switched systems can be modeled for this type of system,and compared with single-mode controllers,switched controllers are easier than handling some more complex systems.For switched systems,different switching mechanisms have a great impact on the system performance,and an inappropriate switching mechanism can even make the system unstable.In addition,as a typical control method,sliding mode control(SMC)is widely used in neural networks,power systems and industrial applications because of its advantages such as strong robustness to disturbances and nonlinearities.To date,there have been fruitful results related to both theories,but the associated SMC problem has not been solved if we refer to the more general persistent dwell-time(PDT)switched systems.Therefore,in this paper,the related SMC design problem will be solved from several perspectives by studying the PDT switched systems in the continuous-time sense.The research content of this paper is as follows:1.For the PDT switched neural networks with unknown disturbances,a synchronous SMC scheme based on the disturbance observer is proposed.Based on the switched Lyapunov stability theory,the SMC theory,and the PDT switching analysis technique,sufficient conditions are obtained to ensure the global uniform asymptotic stability of the sliding mode dynamics with the specified H_∞ performance index,and the specific form of the gain matrices is obtained based on the conventional decoupling method.Moreover,the reachability of the sliding surface is ensured by constructing an SMC law based on a disturbance observer.Finally,a numerical example is used to verify the feasibility of the proposed disturbance observer-based synchronous SMC scheme.2.A switched fuzzy SMC scheme is proposed for the PDT switched T-S fuzzy system.A mode-dependent,fuzzy-dependent and state variable-dependent sliding surface is constructed,and sufficient conditions are derived to ensure the global uniform exponential stability of the sliding mode dynamics by choosing a switched Lyapunov function based on a newer method of handling the normalized membership function.Meanwhile,a switched fuzzy SMC law is synthesized,which can ensure the finite-time reachability of the sliding surface in the presence of external disturbances and uncertainties.Finally,the effectiveness and robustness of the proposed switching fuzzy SMC scheme are verified by a numerical example.3.An adaptive SMC scheme is proposed for the PDT switched nonlinear systems with matching and non-matching uncertainties.Unlike the mode-dependent integral sliding surface constructed earlier,a mode-independent linear sliding surface is constructed here.An adaptive SMC law is designed in order to address the conservativeness of the assumption that the nonlinear upper bound is known in most of the literature.Sufficient conditions,which can ensure that the sliding mode dynamics are globally uniformly exponentially stable,can be obtained with the help of a reduced-order method and a switched Lyapunov function technique.Moreover,the gain matrix is solved by an efficient decoupling approach.Finally,the adaptive sliding mode controller proposed is designed by a numerical example and an RLC series circuit model,and the simulation results satisfy the requirements of the scheme design.