An efficient method for finite time stability calculation of continuous time delay systems

Abstract

This paper provides sufficient conditions for the finite time stability of linear continuous time delay systems mathematically described as x'(t)=A0 x(t) + A1 x(t-τ). A novel method was used to derive new delay dependent conditions. The conditions obtained were applied in the system stability analysis. Consequently, the aggregation function does not have to be positive in the state space domain, and does not need to have the negative derivatives along the system trajectories. Finite time stability was analyzed using the novel conditions derived in the paper. The described approach was compared with some known methods. It was proved that the new results were in compliance with the previously reported results, but more convenient for numerical calculations. The numerical example was presented to support the results.