Observer-based Control And Output Regulation Problems Of Switched Singular Systems

With the development of communication networks,the research of hybrid sys-tems has attracted more and more attention.As an important type of hybrid systems,switched systems are widely applied in large scale power systems,robot control systems,aircraft systems,etc.In addition,due to the affect of external disturbances and parameter uncertainties,nonlinearities axe ubiquitous in system-s.Different from the Lipschitz constants that must be positive,the parameters in quadratically inner-bounded nonlinearity can be negative and zero as well,and quadratically inner-bounded nonlinearity only needs to satisfy the second item of one-sided Lipschitz nonlinear property.Therefore it covers a more general type of nonlinear functions,and it is widely applied in recurrent neural networks,Chua's circuit,Lorentz systems and so on.In this paper,we use the switched singular sys-tems as models to discuss the observer-based finite time stabilization,asynchronous H? control for switched singular systems with quadratically inner-bounded nonlin-earities,and the output regulation problems for linear switched singular systems.The main content is divided into the following seven chapters.In Chapter 1,the research background and research status at home and abroad of switched singular systems,nonlinear systems together with the output regulation problems,observer design and observer-based control problems axe introduced,sev-eral lemmas used in this paper axe given,and the main work and contributions of this paper are summarized.In Chapter 2,the observer-based finite time stabilization for discrete time switched singular systems with quadratically inner-bounded nonlinearities is in-vestigated.By using the Lyapunov functional method and free-weighting matrix te.chnique,sufficient conditions are obtained to guarantee the closed-loop system-s be regular,causal and uniformly finite time bounded under average dwell time switching,the existence and uniqueness of solution for the closed-loop systems is proved by the implicit function theorem simultaneously.The above conditions are transformed into linear matrix inequalities(LMIs)by using the restricted system e-quivalent transformation and matrix decoupling techniques and the observer design methods are given.Finally,numerical examples are given to verify the effective-ness of the proposed methods.The results of this chapter has been published in International Journal of Robust and Nonlinear Control(2019).In Chapter 3,the finite time stabilization for continuous time switched singular systems with quadratically inner-bounded nonlinearities is discussed.Under state feedback and observer based control,solvable conditions are proposed to guaran-tee the closed-loop systems be regular,impulse-free,have a unique solution and be uniformly finite time bounded,and the design methods of these two controller-s are given respectively.Since quadratically inner-bounded nonlinearities contain Lipschitz and one-sided Lipschitz nonlinearities as two special cases,the methods in Chapters 2-3 are also suitable for switched singular systems with Lipschitz and one-sided Lipschitz nonlinear terms.The results of this chapter has been published in the 38th Chinese Control Conference(CCC2019).In Chapter 4,the observer-based asynchronous H? control for a class of discrete time nonlinear switched singular systems is investigated.By selecting the Lyapunov functional which allows increasing before decreasing when a subsystem is active,less conservative stability conditions which also satisfy the H? performance are obtained via average dwell time method and free-weighting matrix approach.By means of Finsler's lemma,the above conditions are transformed into LMIs and the observer design methods are given.Finally,two examples are given to illustrate the applications and advantages of the proposed approaches.The results of this chapter has been published in Journal of the Franklin Institute(2020).In Chapter 5,the output regulation problem for switched singular systems based on error-feedback controller is addressed.Under several basic assumptions,by in-troducing coordinate transformation,the output regulation problem of switched sin-gular systems is transformed into the stability problem of an autonomous system.By using Lyapunov stability theory,solvable conditions of the output regulation problem are developed under average dwell time switching,and the existence con-ditions and parameterized representation for the solutions of the regulator equation are given.Based on that,by using Finsler's lemma,solvable LMI conditions are proposed for the output regulation of switched singular systems and the error feed-back controllers are designed.Finally,numerical examples are given to show the effectiveness of the proposed methods.In Chapter 6,the output regulation of switched singular systems is considered based on full-order and reduced-order observer.By introducing the singular full-order observer to estimate the state and disturbance of the systems simultaneously,under proper assumptions,solvable conditions are obtained of the output regulation problem for switched singular systems and the full-order observer design methods are proposed.The restricted system equivalent transformation is made to the original systems,by employing a reduced-order normal observer,solvable conditions are proposed and the reduced-order observer design methods are given.Finally,an example is given to show the correctness of the proposed methods.In Chapter 7,the main work of this paper is summarized,the disadvantages and shortcomings are analyzed,and the future is prospected.