Robust control of uncertain time-delay systems.

摘要

This work addresses the problem of robust stabilization and robust Hinfinity control of uncertain time-delay systems. The time-delays are considered to be present in the states and/or the outputs, and the uncertainties in the system representation are of the parametric norm-bounded type. Both cases of actuators, with and without saturation are studied, and the state-feedback and output-feedback control designs are presented. Two methods for analysis and synthesis of controllers are used: The first is based on the transfer function, and the second on the use of functionals.; In the context of the design method based on transfer functions, the problem of Hinfinity output feedback design for a class of uncertain linear continuous-time or discrete-time systems, with delayed states and/or outputs (only for the continuous-time case), and norm-bounded parametric uncertainties is considered. The objective is to design a linear output feedback controller such that, for the unknown state and output time-delays and all admissible norm-bounded parameter uncertainties, the feedback system remains robustly stable and the transfer function from the exogenous disturbances to the state-error outputs meets the prescribed Hinfinity norm upper-bound constraint. The output feedback structure does not depend on the time-delay. The conditions for the existence of the desired robust Hinfinity output feedback and the analytical expression of these controllers, are then characterized in terms of matrix Riccati-type inequalities. In the continuous-time context, both the time-invariant and the time-varying cases are treated. Finally, examples are presented to demonstrate the validity and the solvability of the proposed design methods.; Still in the same context, the state-feedback robust stabilization problem for neutral systems with time-varying delays and saturating actuators is addressed. The systems considered are continuous-time, with parametric uncertainties entering all the matrices in the system representation. The model used for the representation of actuator saturations is that of differential inclusions. A saturating control law is designed and a region of initial conditions is specified within which local asymptotic stability of the closed-loop system is ensured.; Finally, the robust output-feedback stabilization problem for state-delayed systems with time-varying delays and saturating actuators is addressed. The systems considered are again continuous-time, with parametric uncertainties entering all the matrices in the system representation. Two models are used for the representation of actuator saturations: sector modeling and differential inclusions. Saturating control laws are designed, and in the case of differential inclusions, a region of initial conditions is specified within which local asymptotic stability of the closed-loop system is ensured. (Abstract shortened by UMI.)