A new approach to stability of singular time delay systems in the sense of non-Lyapunov delay independent conditions

This paper provides sufficient conditions for both practical stability and finite time stability of linear singular continuous time delay systems which can be mathematically described as Eẋ(t) = A₀x(t) + A₁x(t - τ). Considering a finite time stability concept, new delay independent conditions have been derived using the approach based on the Lyapunov-like functions and their properties on the subspace of consistent initial conditions. These functions do not need to have the properties of positivity in the whole state space and negative derivatives along the system trajectories. When the practical stability has been analyzed the above mentioned approach was combined and supported by the classical Lyapunov technique to guarantee the attractivity property of the system behavior.