On the Structure of a Liapunov Functional for a Difference-Differential Equation with One Delay.

摘要

A quadratic positive definite Liapunov functional that yields necessary and sufficient conditions for the asymptotic stability of the solutions of the matrix difference-differential equation dx(t)dt = Ax(t) + Bx(t-tau) is constructed and its structure is analyzed. The method of construction is a natural generalization of the same problem for an ordinary differential equation, and this relationship is emphasized. (Author)