Delay-dependent conditions for finite time stability of continuous systems with latency

In the present study, the practical and finite time stability of linear continuous system with latency has been investigated. The proposed result outlines the novel sufficient stability conditions for the systems represented by the following equation: x´(t)=A₀x(t) - A₁x(t - τ). The results can be applied to the analysis of both the practical and finite time stability of the continuous systems with time delay. For the derivation of the finite time stability conditions, the Lyapunov-Krassovski functionals were used. Unlike in the previously reported results, the functionals did not have to satisfy some strict mathematical conditions, such as positivity in the whole state space and possession of the negative derivatives along the system state trajectories. The numerical examples presented in this study additionally clarified the implementation of the methodology, and the calculations of the stability conditions. Generally, it was found that the proposed sufficient conditions were less restrictive compared to the ones previously reported.