Analysis And Synthesis Of Switched Systems Based On Non-monotonic Lyapunov Functional

As a special class of hybrid dynamical systems,switched systems have been a hot topic in control community due to their wide applications and special dynamic behavior.Generally,a typical switched system consists of a family of subsystems and a rule orchestrating the switching between them.Different from common time-varying systems,the solutions of switching differential equations subject to switching behaviors are dependent on both system initial conditions and switching signals,which further complicates the research work.The average dwell time(ADT)switching has been demonstrated to be a flexible and effective switching logic for stability analysis and controller synthesis.However,the ADT switching approach requires a monotonic decrease of Lyapunov functional(LF).To this end,this paper investigates a non-monotonic LF approach,which allows a non-monotonic behavior both at the switching instants and during the running time of each subsystem.The main work of this thesis are summarized as follows:(1)The concept of non-monotonic LF is introduced to the switched systems and the two-step non-monotonic LF approach is developed to analyze a class of discrete-time uncertain switched systems.Such an approach allows the LF to increase during the running time of subsystems,but guarantees an average decrease on every two sampling steps.By seeking the exponential decaying law of decreasing points of LF,sufficient conditions with globally uniformly asymptotical stability guarantee are addressed and a robust controller is further designed.The proposed approach achieves larger stability region as well as better H? performance.(2)Based on the two-step LF approach,the N-step non-monotonic approach is further studied for conservatism reduction in stability criterion and controller design.By introducing auxiliary variables and predictive horizon,the difficulties in dealing with the future exogenous noises can be properly resolved by solving a set of linear matrix inequalities(LMIs).With the increasing of number N,stability criterion can be improved as well as the capability of disturbance attenuation.The relationship between the N-step time difference of LF and ADT constraint is thoroughly discussed.(3)To improve the H? filtering performance,a non-monotonic LF approach is proposed to design a robust H? filter for a class of switched systems.The filtering performance can be improved,while as a cost,the ADT constraint of the switching law should be more critical at the same time.To further relax the restriction on the switching law,the mode-dependent ADT switching is introduced such that a trade-off between the switching frequency and filtering performance can be achieved.A co-design of the filter and switching law can be obtained by the developed approach.(4)The non-monotonic LF approach is extened for conservatism reduction in dissipative dynamic output feedback(DOF)controller design.First,the dissipativity criteria are derived based on a unified analysis framework.Similar to the stability results,a larger dissipative region can be achieved by increasing the predictive step N.Then,a robust dissipative DOF controller is further designed based on the dissipative analysis.Unlike the traditional method that introduces equality constraint to formulate numerical testable conditions with heuristic nature,a less conservative controller design is adopted,where the LF matrix is formulated without structural constraint.