Finite-Time Stability Analysis of Descriptor Discrete Time-Delay Systems Using Discrete Convolution of Delayed States

Abstract

This paper provides sufficient conditions for the finite time stability of linear time invariant discrete descriptor time delay systems, mathematically described as Ex(k+1) = A(0)x(k) + A(1)x(t-h). A novel method was used to derive new delay dependent conditions. Stability of the system was analyzed using both the Lyapunov-like approach and the Jensen's inequality, including convolution of delayed states. The established conditions were applied to analysis of the system stability. In this case, the aggregation functional does not have to be positive in the state space domain and does not need to have the negative derivatives along the system trajectories. The system stability conditions were applicable to investigation of the finite time stability using the novel conditions proposed in this paper. This mathematical formulation guaranteed that the states of the systems do not exceed the predefined boundaries over a finite time interval.