Robust control of uncertain time-delay systems

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.