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.
— Necessary conditions for the exponential stability of linear systems with distributed delays are presented. The originality of these conditions is that they depend only on the system Lyapunov delay matrix which is a central concept of the so-called complete type Lyapunov-Krasovskii functional approach. The result is validated by some examples.
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)