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This paper is concerned with the problem of stability analysis of two-dimensional (2-D) descriptor systems described by a Roesser-type model with generalized directional time-varying delays. By constructing an improved 2-D Lyapunov–Krasovskii functional candidate and utilizing zero-type free matrix equations, new delay-dependent conditions are derived in terms of linear matrix inequalities (LMIs) to ensure that the system under consideration is regular, causal and internally stable. The obtained results are shown to extend the existing literature by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, the problem of reachable set estimation of two-dimensional (2-D) discrete-time systems described by the Roesser model with interval time-varying delays is considered for the first time. New 2-D weighted summation inequalities, which provide a tighter lower bound than the commonly used Jensen summation inequality, are proposed. Based on the Lyapunov-Krasovskii functional approach, and by using the 2-D weighted summation inequalities presented in this paper, new delay-dependent conditions are derived to ensure the existence of an ellipsoid that bounds the system states in the presence of bounded disturbances. The derived conditions are expressed in terms of linear matrix inequalities, which can be solved by various computational tools to determine a smallest possible ellipsoidal bound. Applications to exponential stability analysis of 2-D systems with delays are also presented. The effectiveness of the obtained results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, a periodic SI model with delays is studied. By utilizing the Lyapunov–Krasovskii functional method, a novel explicit criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is established. Finally, a numerical example is given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract: In this note, the problem of state bounding for linear time-varying systems with delay and bounded disturbances input is considered for the first time. By using a novel approach which does not involve the Lyapunov–Krasovskii functional method, new explicit delay-independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it. A numerical example is given to illustrate the effectiveness of the obtained result. [Copyright &y& Elsevier]

This article presents new exponential stability and stabilisation conditions for Takagi-Sugeno fuzzy time-varying delay systems. Based on an improved Lyapunov-Krasovskii functional, the exponential stability and stabilisation conditions are derived in terms of linear matrix inequalities, which allows one to compute simultaneously the two bounds that characterise the exponential stability rate of the solution. Finally, some numerical examples are given to illustrate the effectiveness of the proposed conditions. [ABSTRACT FROM AUTHOR]