Finite time stability of continuous time delay systems: Jensen's inequality-based approach

In this study, finite-time stability of the linear continuous time-delay systems was investigated. A novel formulation of the Lyapunov-like function was used to develop a new sufficient delay-dependent condition for finite-time stability. The proposed function does not need to be positive-definite in the whole state space, and it does not need to have negative derivatives along the system trajectories. The proposed method was compared with the previously developed and reported methodologies. It was concluded that the stability investigation using the novel condition for stability investigation was less complicated for numerical calculations. Furthermore, it gives comparable results in comparison with the ones obtained with other analyzed conditions, and it provides superior results for some systems.