Further results on the construction of strict Lyapunov–Krasovskii functionals for time-varying time-delay systems

This paper is concerned with the construction of strict Lyapunov–Krasovskii functionals (LKFs) for analyzing the input-to-state stability (ISS) problem of nonlinear time-varying time-delay systems. With the help of a known non-strict LKF, a series of strict LKFs are constructed for both continuous and discrete time-varying time-delay systems. The proposed LKFs are linear functionals of the known non-strict LKF. Compared with previous results, the proposed strict LKFs are more general. Taking advantage of the concepts of uniformly exponentially stable (UES) and uniformly exponentially expanding (UEE), the assumption of boundedness on the scalar function is not required. The effectiveness of the proposed theoretical results is illustrated by a couple of numerical examples.