On finite time stability and asymptotic practical stability of time delayed systems: New delay dependent criteria

This paper gives sufficient conditions for the practical and finite time stability of linear continuous time delay systems of the form ẋ(t) = A₀x(t) + A₁x(t - τ). When we consider finite time stability, these new, delay independent conditions are derived using the approach based on Lyapunov-Krassovski functionals. In this case these functionals need not to have: a) properties of positivity in whole state space and b) negative derivatives along system trajectories. When we consider concept of practical stability, before mentioned concept of stability, is combined and supported by classical Lyapunov technique to guarantee attractivity properties of system behavior.