Asymptotic practical stability of time delay systems

This paper provides sufficient conditions for the asymptotic practical and finite time stability of linear continuous time delay systems mathematically described as x´(t)= A₀x(t) - A₁x(t - τ). The Lyapunov-Krassovski functionals were used to establish the novel delay independent conditions. These conditions were applied in the system stability analysis. Consequently, the functionals do not have to be positive in the whole state space, and they do not need to have negative derivatives along the system trajectories. Practical stability was analyzed using the derived novel conditions. The described approach was combined with the classical Lyapunov technique to guarantee the attractive practical stability of the system.