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In the existing papers considering the stability analysis of discrete-time systems with distributed delays via the Lyapunov-Krasovskii functional (LKF) method, the delay kernels are normally restricted to be non-negative. In this paper, we aim to remove such a restriction and deal with the stability analysis of systems with arbitrary delay kernels. For this purpose, a kernel-related summation inequality is first constructed. Then, a stability condition is derived based on the proposed inequality and a model transformation. Finally, two numerical examples are presented to show that the proposed stability condition not only has a wider scope of application and is less conservative than the existing ones. [ABSTRACT FROM AUTHOR]

In this paper, a Bessel-type inequality in semi-inner produce (s.i.p.) spaces is presented to deal with the problem of stability analysis for a class of discrete-time systems with distributed delays. The main purpose of this paper is to obtain less conservative stability conditions for the investigated systems. For this purpose, a novel inequality (which is referred to as Bessel-type inequality in s.i.p. spaces) is constructed by combining the Bessel inequality and a set of polynomials which is pairwise orthogonal in a s.i.p. space. The proposed inequality is more general than the conventional Jensen-type inequality, which is, to the best of our knowledge, the only inequality to deal with the problem of stability analysis for discrete-time systems with distributed delays up to now. Based on the proposed inequality and the Lyapunov-Krasovskii stability theory, a stability condition is presented. Finally, a numerical example is given to indicate that the proposed method is able to effectively reduce the conservatism. [ABSTRACT FROM AUTHOR]