Output Regulation Of Time-varying Delay Systems And Singular Multi-agent Systems

The output regulation problem is one of the most important issues in control theory, which involves internal stabilization of systems, tracking reference control and disturbance rejection. The output regulation problem, or alternatively, the servomechanism problem, addresses design of a feedback controller to achieve asymptotic tracking for a class of reference inputs and disturbance rejection for a class of disturbances in an uncertain system while maintaining closed-loop stability. Output regulation of linear time-varying delay systems and linear singular multi-agent systems are considered respectively. The main contributions are as follows:Firstly, aimed at output regulation of linear time-varying delay systems, integral controller design is studied. By introducing the integral inequality and reciprocal convex combination approach to construct an augmented Lyapunov-Krasovskii functional, a new delay-independent stability criteria is presented based on strict linear matrix inequalities(LMIs). The solvability problem of the output regulation equation with time-varying delay is converted into tracking the output error problem.Sufficient condition for the solvability of the tracking error problem is obtained.Secondly, the output regulation problem of linear singular multi-agent systems by both states feedback control and time-delay feedback control is considered. As for states feedback, a rapid subsystem is obtained by a standard coordinate transformation.The sufficient conditions for output regulation of singular multi-agent systems are presented by studying the stabilization of rapid subsystem and the solvability of regulators equation. As for time-delay feedback, a new Lyapunov function candidate is constructed to solve the stabilization problem of linear singular multi-agent systems;Regulators equation is converted into the form of a non-homogeneous equation AX=B,the sufficient condition for the solvability of the tracking error is provided by using Kronecker product and Jordan canonical form to prove that the matrix A is full rank.