In this paper we demonstrate how Lyapunov-Krasovskii functionals can be used to obtain exponential bounds for the solutions of time-invariant linear delay systems.
we can see (x 3 t) 2 (zt) 2 by the comparison theorem . Hence, = 1. By the monotonicity of u 0 (x) and '(x), the uniqueness of (28) holds. Thus, we conclude that (28) admits a unique strong solution (x 3 t). Now, we apply Ito's formula for convex functions [7, p. 219] to obtain e 0t u(x 3 t) = u(x) + t 0 e 0s 0u + Axu 0 +c 3 s u 0 + 1 2 2 x 2 u 00 x=x ds… (More)