On finite time stability of continuous time delayed systems: New delay dependent conditions

In this paper, we analyzed the finite time and practical stability of the invariant linear continuous systems with time delay forumlated as x´(t) = A₀ x(t) + A₁ × (t-τ). The sufficient stability conditions were presented for this class of systems. The derivation of the novel delay independent conditions for the finite time stability of such systems was performed using the Lyapunov-Krassovski functional. In this approach, the functional did not need: a) to be positive in the entire state-space and b) to have negative derivatives along the trajectories of the system. The numerical example and the system simulation were performed to demonstrate the applicability of the derived stability conditions.