Stability criteria for linear time-invariant systems with multiple delays

Two new asymptotic stability criteria for linear time-invariant systems with multiple delays are established by using a quadratic inequality lemma together with frequency-domain techniques. One criterion is for delay-dependent α-stability and another is for delay-independent asymptotic stability. 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. In addition, it is remarked that the established delay-independent asymptotic stability criterion with one tuning parameter matrix P > 0 improves and simplifies the existing criterion with more than one tuning parameter matrix in the literature.

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