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This study is concerned with the problem of stability analysis of two‐dimensional (2D) discrete‐time Roesser systems with time‐varying delays. First, based on an augmented Lyapunov–Krosovskii functional, a less conservative stability criterion incorporating time‐varying terms is established by utilising a general free‐matrix‐based inequality. Next, in order to eliminate the time‐varying terms without introducing redundant constraints, a quasi‐convex combination method is proposed. Then, compared with the criteria derived via the other inequalities, the conservatism analysis is given to prove the proposed criterion can lead to a better result theoretically. Finally, a numerical example is presented to illustrate the advantage of the presented method. [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]