A Linear Matrix Inequality Approach to Robust Stability Conditions for Linear Time-Delay Systems

Abstract

The robust stability problem for a class of uncertain linear systems with time-varying delays in the state is discussed. The uncertainty is assumed to be norm-bounded and appears in all matrices of the state-space model. A robust stability condition being dependent on the length of the delay is derived in the form of linear matrix inequalities (LMIs), which is less conservative than several previous delay independent or delay dependent conditions.