Robust Absolute Stability Analysis of Multiple Time-Delay Lur'e Systems With Parametric Uncertainties

The problem of robust absolute stability for time-delay Lur’e systems with parametric uncertainties is investigated in this paper. The nonlinear part of the Lur’e system is assumed to be both time-invariant and time-varying. The structure of uncertainty is a general case that includes norm-bounded uncertainty. Based on the Lyapunov–Krasovskii stability theory, some delaydependent sufficient conditions for the robust absolute stability of the Lur’e system will be derived and expressed in the form of linear matrix inequalities (LMIs). These conditions reduce the conservativeness in computing the upper bound of the maximum allowed delay in many cases. Numerical examples are given to show that the proposed stability criteria are less conservative than those reported in the established literatures.

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