Stability of Discrete-Time Systems with Time-Varying Delay: Delay Decomposition Approach

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

New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature