Robust Passive Control For Uncertain Systems With Time-delays

Dissipative systems theory plays an important part in the stability analysis.Its essential content is being a nonnegative energy function, which makes the energy consumption of the system, is less than the energy provision.In the practical system, the passivity is a special example of dissipative systems.We consider the passivity of systems in which supply rate is represented by the product of the system input and output.Under mild regularity assumptions, we design a state feedback controller and output feedback controller, identifying Lyapunov function of these uncertain time-delay linear systems, to guarantee the passivity of the closed-loop system.This paper focuses on the passivity of some classes of uncertain time-delay systems.In terms of a linear matrix inequality (LMI), the sufficient conditions for the solvability of this problem are presented.Based on Lyapunov stability theory, for the uncertain time-delay systems, the major contributions of this dissertation are as follows:(1) A class of linear time-varying delay systems are considered.A state feedback passive controller and output feedback passive controller for linear systems with time-varying delays in state and control input are proposed.(2) A class of uncertain linear systems with delayed state and parameter uncertainties are dealt.This problem aims at designing the linear state observers such that, for all admissible parameter uncertainties, the observation process remains robustly stable and passive, independently of the time delay.An effective matrix inequality methodology is developed to solve the proposed problem.We derive the conditions for the existence of the desired robust passive observers.(3) A class of linear neutral systems with time-delays and parameter uncertainties are developed.The Lyapunov and LMI method are developed to consider the problem of robust passive control. We derive the conditions for the existence of the desired robust passive controllers to make the system be stable.(4) A class of discrete-time systems with time-varying uncertainties in the state are solved.We derive the conditions for the existence of the system to be stable and strict passive, then design the state-feedback controller and dynamic output-feedback controller.