The problem of designing dynamic controllers for a class of linear dynamical systems with time-varying delays subject to input disturbance as well as output measurement error and in which some parameters are unknown-but-bounded is considered. It is establishing that when certain structural constraints are met, then two stabilizing controllers can be constructed to render the closed-loop system 'globally practically stable'. The controllers have three terms: a growth term, an output-driven term and a nonlinear term. Robustness of the developed dynamic controllers against mismatched uncertainties is also proved. Simulation studies are carried out on a water-quality model to illustrate the potential of the control methodology. KEY WORDS uncertain systems; state delay; output feedback; dynamic control; global practical stability
1. Introduction
The control problem addressed in this article can be phrased as follows: Given a class of linear dynamical systems with time-varying state delays in which the system and input matrices have uncertain (unknown-but-bounded) parameters and subject to input disturbance and output measurement error. It is required to construct an output feedback control for this class of systems such that the resulting closed-loop system attains desirable system properties. Solution of this problem falls within the general area of 'robust control design'.
There have been several approaches to the design of robust controllers, including Hatheory'-3 and the deterministic framework of Corless and L e i t m a ~~n . ~
The main aspects of the latter framework, which will be followed in this work, are:
(1) no statistical characterization of the uncertainties is needed, (2) the uncertainty may be time-varying (possibly fast) and nonrepetitive, (3) only the bounds on the uncertainties are assumed available, and (4) certain properties of the 'nominal' system (when all of the uncertainties are suppressed) Major development along this direction, from the viewpoint of the present work, can be divided into two categories. The first category treats systems without state-delay and includes, amongst many others, the work of Corless and Leitmann,' Chen and Leitmann,6 Leitmann,' Barmish' and Ryan.' The second category deals with time-delay systems and the related work This paper was recoinmended f o r publication by editor M. J . Grirnble are identified for initial design.