Abstract
The Lyapunov matrix is a key element of the construction of Lyapunov–Krasovskii functionals with prescribed derivative for linear time-invariant time delay systems. Moreover, stability criteria which are based exclusively on the Lyapunov matrix have been developed recently. A weak point of the approach is a lack of effective techniques to compute the Lyapunov matrix when the delays are incommensurate, i.e. at least two of them are rationally independent. To overcome this difficulty, we present in this paper necessary stability conditions for systems with incommensurate delays based on the Lyapunov matrix of a “close” auxiliary system with commensurate delays, which can be computed by known techniques. An explicit condition for the choice of delays of the auxiliary system is provided. Illustrative examples are given.
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