Study On Stabilization And Anti-disturbance Control Of Switched Systems Based On Multiple Lyapunov Functions Methods

As an important and special class of hybrid systems,switched systems are of great significance both in theory development and engineering applications.Switched systems have attracted increasing attention.A rapid progress has been made so far,most of the results on switched systems focus on stability and stabilizability.However,due to the complexity arising from interaction between the continuous dynamics and discrete dy-namics,coupled with the co-design of controllers of subsystems and switching signals,the dynamic behavior of switched systems become very complicated and this makes the design of switched systems very difficult.Thus a lot of problems deserve investigation.On the other hand,stabilization and anti-disturbance control,as important system proper-ties,have been widely applied in the analysis and design of non-switched systems and a systematical theory has been established.For switched systems,especially for switched LPV systems,the study on anti-disturbance control is just at the early stage.Many prob-lems are far from being understood and thus deserve investigation.This dissertation studies a few synthesis issues of switched systems including com-posite anti-disturbance control,output tracking control,resilient control,bumpless trans-fer,guaranteed cost control,output regulation and dissipativity.The main contributions are as follows.1.The problem of composite anti-disturbance control for switched linear systems with multiple disturbances is investigated via the multiple Lyapunov functions method.Firstly,a mixed state-dependent and time-driven switching strategy is designed,and it guarantees a dwell time even when the problem of anti-disturbance control of all subsys-tems are unsolvable.Then,the disturbance observer and the state-feedback controller are constructed with the help of the designed switching law to guarantee the asymptotic sta-bility of the closed loop system,and attenuate the effect of different types of disturbances.2.The issue of H? output tracking control for a class of switched LPV systems is s-tudied.A set of parameter and mode-dependent switching signals are designed and a fam-ily of switching LPV controllers are developed using the multiple parameter-dependent Lyapunov functions method,and a sufficient condition for H? output tracking control of switched LPV systems is given.The solvability of the H? output tracking control problem for individual subsystem is not assumed.Unlike the existing results where the switching law is parameter-independent,the proposed switching law and controller are parameter-dependent.3.The problem of H? resilient control for a class of switched LPV systems by utiliz-ing a multiple parameter-dependent Lyapunov functions method is investigated.When the system states are available,a resilient observer,an observer-based resilient controller and a parameter and estimate state-dependent switching signal which can guarantee asymp-totic stability for the given systems are designed.In order to achieve the disturbance attenuation,the designed observer and controller are non-fragile,so the proposed control strategy is strong in robustness.4.The problem of H? bumpless transfer for a class of switched LPV systems is ad-dressed for the control discontinuities and bumpy in a practical situation.A set of switch-ing signals depending on parameters and modes are designed and a family of switching LPV controllers are developed.Even though the bumps limitation constraint for each subsystem is unsatisfied,the restriction for switched LPV systems is still satisfied by the designed controllers and the designed switching law.5.The dissipativity and related properties for switched LPV systems by using mul-tiple parameter-dependent storage functions and parameter-dependent supply rates is in-vestigated.Firstly,a novel concept relating to external parameters is proposed to describe the overall dissipativity property of switched parameter-varying systems in the absence of the conventional dissipativity property of the subsystems.Secondly,several classic forms of dissipativity:parameter-dependent QSR-dissipativity,passivity and generalized L2-gain,are addressed.Unlike the classical storage functions methods,the proposed mul-tiple parameter-dependent storage functions method gets rid of the decreasing assumption of storage functions on the switching times.6.The guaranteed cost control problem for switched LPV systems is investigated.Firstly,a parameter and state-dependent switching strategy is designed,and it guarantees a dwell time even when all subsystems are unstable.Then,a sufficient condition ensuring the guaranteed cost control for switched LPV systems is presented via proper multiple parameter-dependent Lyapunov functions matching different time intervals.Further,the parameter-dependent controller is constructed to guarantee the asymptotical stability of the closed-loop system,and guaranteed cost index is achieved.7.The output regulation problem for switched LPV systems with Markovian jump parameters under partially unknown transition probabilities is dealt with.When the sys-tem states are available,the first part gives the sufficient conditions which guarantee s-tochastic stability of the closed loop system and the regulated output asymptotically tends to zero.The second part focuses on the case that the system states are not available.By using parameter-dependent stochastic Lyapunov functions,a sufficient condition is obtained,and a regulation observer-based controller are designed such that the output regulator problem for switched LPV systems is solvable.8.The asymptotical stability for switched nonlinear systems via a ratio-type multiple Lyapunov functions method is studied.As an application of the ratio-type multiple Lya-punov functions method,the asymptotical stability has been studied by the dual design of the switching law and the controllers for a class of switched nonlinear systems.Unlike the traditional multiple Lyapunov functions method,the ratio-type multiple Lyapunov func-tions method is more flexible in that the connecting of the adjacent Lyapunov functions is no longer assumed and the Lyapunov functions are allowed growth in arbitrarily many finite number of consecutive switching points.This characteristic provides more freedom for the choice of multiple Lyapunov functions.The conclusions and perspectives are presented in the end of the thesis.