Contents 1 Introduction
Time-delay phenomenon is ubiquitous in real life and has impacts on the stability of systems [1], [8], [1]–6, [17], [23]. For example, genetic regulatory networks [9], [27], [28]–, neutral-type time-delay systems [7], [22], [24]–, T-S fuzzy systems [12], [15], [21]–, discrete-time time-delay systems [6], [19], [25]–. Because the linear discrete-time systems are very important in the compute simulations of the continuous-time systems, the stability analysis of the linear discrete-time systems has received widespread attention in recent years (see [1]–6, 11, 13, 14, 16, 18,20,[26] and the references therein). Especially, the exponential stability analysis of the linear discrete-time systems becomes the focus of control field. For example, the Lyapunov stable analysis and exponential convergence estimates for linear discrete-time systems are introduced in [1]. The exponential stability of linear discrete-time systems with single delay is obtained in [4], [5]. Specially, the exponential stability analysis in LKFs framework and the exponential decay rate estimates of the linear discrete-time systems with multiple delays were given in [3]. The sufficient condition for the exponential stability of a set of perturbed time-varying difference equations with multiple delays is obtained in [13], which has established specific criteria for global exponential stability. Some sufficient conditions ensuring th moment exponential stability of the second-order stochastic neutral partial functional differential equations driven by impulsive noises are obtained in [10]. The robustness of the exponential stability in Hilbert spaces is established [14]. WDOPs-based summation inequality can be employed to obtain the exponential stability criteria and explicit exponential estimates of all solutions of linear delay difference systems with single constant delay in [26]. However, with the increase of the system matrices dimension and the number of time delays, it is difficult to compute its decay rate for systems. Based on the above reasons, the results in [26] are generalized to linear discrete-time systems with two constant delays.
