Further Results on Finite-time Stability of Continuous Singular Time Delay Systems

Abstract

This paper provides novel additional sufficient conditions for finite-time stability of the linear continuous singular time delay systems. A novel method was used to derive new delay dependent conditions. The stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's and Coppel's inequality, including the convolution of delayed states. The derived conditions were applied in the system stability analysis. As a result of these, the aggregation functional did not have to be positive in the state space domain and did not need to have the negative derivatives along the system trajectories. Finite-time stability was analyzed using the novel conditions derived in this paper, which guarantees that the states of the systems do not exceed the predefined boundaries over a finite-time interval.