Sufficient Conditions for Robust Stability of Uncertain Discrete Systems With Multiple Time Delays

Abstract

The problem of robust stability of linear discrete systems with multiple time 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 suffi cient condition for robust stability of such uncertain discrete time-delay systems is derived. This new robust stability condition is concerned with a sum of terms each of which involves the ith right eigenvector, the ith left eigenvector, and the absolute value of the ith eigenvalue. It is also shown that the derived sufficient condition is less conservative than those derived by using traditional method. Finally, a numerical example is given to demonstrate the validity of our results.