A new approach to the stability of time-delay systems in the sense of Non-Lyapunov delay-independent and delay-dependent criteria

In this article the sufficient conditions for the practical and finite-time stability of the linear continuous systems with the time-delay are presented. The new delay-independent stability conditions are derived using Lyapunov-like functions for the finite-time systems. For these functions it is not necessary to have properties of positivity in the whole state space as well as negative derivatives along the system trajectories. The proposed approach is supported and combined with classical Lyapunov technique to guarantee actractivity of the system.