Stability criteria for linear time-invariant systems with multiple delays

Two new asymptotic stability criteria for linear time-invariant systems wit h multiple delays are established by using a quadratic inequality lemma tog ether with frequency-domain techniques. One criterion is for delay-dependen t alpha -stability and another is for delay-independent asymptotic stabilit y. Each of them has only one tuning parameter matrix P > 0 as the Lyapunov- type stability criteria for the corresponding linear time-invariant systems without delays do. Both of the established stability criteria are given in the form of LMI problems and hence are very easy to use in applications. I n addition, it is remarked that the established delay-independent asymptoti c stability criterion with one tuning parameter matrix P > 0 improves and s implifies the existing criterion with more than one tuning parameter matrix in the literature. (C) 2000 Academic Press.