A Criterion to Exponential Stability of Dynamic System with Mixed Time-delays Based on LMI

Based on the descriptor system approach and constructing proper Lyapunov functions,an exponential stability condition for dynamic system with mixed time-delays is given,which can be expressed in the form of linear matrix inequality(LMI).By decomposing the coefficient matrix of the delay vector,a less conservative criterion is derived.The exponential decay σ rate which is related to the time delay is obtained by solving a feasibility problem of LMI.Finally,numerical examples are given to show that result is effective.