Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, finite-time stability problem for a class of linear time-varying delay systems is studied. Based on Lyapunov-like functions method and using an appropriate model transformation of the original system, the sufficient delay-dependent finite-time stability conditions are derived. The criteria are presented in the form of LMIs, which are dependent on the minimum and maximum delay bounds. The numerical examples are presented to illustrate the applicability of the developed results

Abstract:This article deals with the problem of obtaining delay-dependent stability conditions for a class of discrete-time systems with interval time-varying delay. Using the decomposition the delay interval into two unequal subintervals by tuning parameter α, a new interval delay-dependent Lyapunov-Krasovskii functional is constructed to derive novel delay-dependent stability conditions which are expressed in terms of linear matrix inequalities. This leads to reduction of conservatism in terms of the upper bounds of the maximum time-delay. The numerical examples show that the obtained result is less conservative than some existing ones in the literature.

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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.

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