Delay-dependent robust absolute stability criteria for uncertain multiple time-delayed Lur'e systems

In this paper, the problem of delay-dependent robust absolute stability of uncertain multiple time-delayed Lur'e systems with sector-bounded nonlinearity is investigated. The nonlinearity is assumed to be both time-invariant and time-varying. Based on the Lyapunov-Krasovskii stability theory and matrix decomposition method, some delay-dependent sufficient conditions for the robust absolute stability of the Lur'e system is derived and expressed in the form of Linear Matrix Inequalities (LMIs). By solving a convex optimization problem for these LMIs, the maximum upper bounds of the allowable delays are obtained. Some numerical examples are given to show that the proposed stability criteria are less conservative than those in the literature.