This paper is concerned with the exponential robust stability and robust stabilization for linear time delayed system and subject to real convex polytopic uncertainty. We propose some new necessary and sufficient conditions in terms of Linear Matrix Inequalities (LMIs) for nominal state delayed systems without uncertainties to be stable by estimating the stability bound of delay decay rate and upper bound delay time. Based on these results, the state feedback stability problem is solved and the result is extended to the case of uncertain delayed systems. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.
Delay systems, exponential stability, robust stabilization, state feedback, uncertain systems, LMI.
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