1996 Volume 32 Issue 1 Pages 8-15
Constant or time-varying delay is often encountered in various engineering systems to be controlled, such as chemical processes, long transmission lines in pneumatic, hydraulic, and rolling mill systems, and the existence of the delay is frequently a source of instability. On the other hand, it is not avoidable to include some degrees of uncertainty in practical control systems due to modelling errors, measurement errors, linearization approximations, and so on. Therefore, the problem of robust control for uncertain dynamical systems with time-delay has received considerable attention, and some solution approaches have been developed.
In this paper, we consider the problem of robust control for linear dynamical systems with both time-varying delay and uncertainties. Firstly, we consider time-delay systems with structured uncertainties, and by employing some analytical methods, derive some sufficient conditions for robust stability of uncertain closed-loop time-delay systems under a memoryless linear feedback controller. Secondly, we extend the above results to time-delay systems with unstructured uncertainties, and discuss some related problems.
It worth pointing out that in this paper, delay is assumed only to be any nonnegative continuous and bounded function on time. Therefore, the results obtained here may be applied to systems with uncertain delays due to the developed sufficient conditions independent of delay. Moreover, a numerical example is given to demonstrate that the robust stability conditions developed in this paper are less conservative than those reported in the control literature.
