Eigenstructure assignment-based robust stability conditions for uncertain systems with multiple time-varying delays

The problem of robust stability of dynamical systems with multiple time-varying delays and structured state-space uncertainties is discussed. Based on the fact that the dynamic response of a multivariable control system can be modified by means of eigenstructure assignment, a method is presented whereby a new sufficient condition for robust stability of such uncertain time-delay systems is derived. The new robust stability condition is a sum of terms, each of which involves the ith right eigenvector, the ith left eigenvector, and the real part of the ith eigenvalue, and is shown to be less conservative than the earlier result reported in the control literature. Here, each time-varying delay is assumed only to be any bounded, continuous non-negative function, and the derived robust stability condition is independent of the delay. Therefore our results are also applicable to systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results. (C) 1997 Elsevier Science Ltd.