A Study Of The Output Regulation Problem For A Class Of Descriptor Time-varying Systems

With the continuous in-depth study of descriptor systems,scholars have shifted the scope of research from general descriptor time-invariant systems to more extensive descriptor timevarying systems.The output regulation problem is one of the important research topics in control theory.The output regulation problem of descriptor time-invariant systems is important for the study of systems such as power networks,aerospace engineering,and robotic arm operation.This paper investigates the output regulation problem of descriptor time-varying systems based on the regulator equation and the internal mode principle.The output regulation problem of the system is studied for the descriptor time-varying system.Firstly,a regulator equation with the form of a differential algebraic matrix equation is proposed for the descriptor time-varying system.The unique solution of the regulator equation is obtained based on the equivalent transformation of the descriptor time-varying system.Secondly,based on the regulator equation,a state feedback controller and a dynamic measurement output feedback controller are designed to obtain sufficient necessary conditions for the solvability of the output regulation problem of the descriptor time-varying system.Finally,the effectiveness of the method is verified by numerical calculations.The problem of robust output regulation of the system is investigated for a descriptor time-varying system containing uncertainty.Firstly,for the descriptor time-varying system containing uncertainty,an internal model of the descriptor time-varying system is obtained by designing a new feedback mechanism to immerse the external system into the descriptor timevarying system based on the nature of consistent observability.This model allows the system under study to generate control inputs with errors asymptotically converging to zero automatically.Secondly,the controllability and observability of the system are analyzed to obtain sufficient conditions for the consistent asymptotic stability of the closed-loop system.Finally,the effectiveness of the proposed method is demonstrated by numerical examples.