Necessary conditions for the exponential stability of one delay linear systems expressed in terms of the Lyapunov matrix of the system are proved. The effectiveness of the proposed conditions is shown in illustrative examples.
This paper deals with linear time-invariant systems with multiple delays. We present a necessary and sufficient stability condition, expressed in terms of the delay Lyapunov matrix. This result generalizes the well known Lyapunov theorem for delay free linear systems. An illustrative example shows how to apply the presented condition.
Necessary conditions for the exponential stability of one delay linear systems are proved. These conditions depend exclusively on the Lyapunov matrix of the delay system, thus improving previous results which were expressed not only in terms of the Lyapunov matrix, but also on system matrices. They are obtained via the substitution of a special initial… (More)