Abstract
The problem of robust stability of time-delay system with structured state space uncertainties is discussed. A method is presented whereby a new class of sufficient conditions for robust stability of such an uncertain time-delay system are derived. It is shown that the stability robustness of such a system can be ensured provided that the eigenvalues of nominal closed-loop system (i.e. the closed-loop system in the absence of uncertainty and delay) lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainties (including those corresponding to delayed state) and the eigenvector matrix of nominal closed-loop system. It is also shown that for time-delay systems with structured state space uncertainties, the robust stability condition derived here is less conservative than those reported in the control literature.
In addition, we only assume that the time-varying delay is a bounded and continuous function, and the robust stability condition derived here is independent of the delay. Therefore, our results are also applicable to systems with perturbed time-delay. Finally, a numerical example is given to demonstrate the validity of our results.
