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In this chapter, the problems of stability analysis and controller design are presented for some classes of discrete-time 2-D systems with directional state delays. Inspired by the conventional Lyapunov–Krasovskii functional method, an analysis scheme is first developed. The proposed scheme is then utilized in combination with extended 2-D summation inequalities to derive delay-dependent stability conditions in terms of linear matrix inequalities for 2-D Roesser systems with interval delays. Analogous results for 2-D in Fornasini–Marchesini model with delays are also discussed. On the basis of stability conditions, the stabilization problems via conventional state-feedback controllers and event-triggered state-feedback controllers are presented. The effectiveness of the obtained results is illustrated by numerical examples and simulations.

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Stability and Stabilization of Two-Dimensional Systems with State Delays

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  • 发表日期：

    2025年

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  • Le Van Hien

摘要

In this chapter, the problems of stability analysis and controller design are presented for some classes of discrete-time 2-D systems with directional state delays. Inspired by the conventional Lyapunov–Krasovskii functional method, an analysis scheme is first developed. The proposed scheme is then utilized in combination with extended 2-D summation inequalities to derive delay-dependent stability conditions in terms of linear matrix inequalities for 2-D Roesser systems with interval delays. Analogous results for 2-D in Fornasini–Marchesini model with delays are also discussed. On the basis of stability conditions, the stabilization problems via conventional state-feedback controllers and event-triggered state-feedback controllers are presented. The effectiveness of the obtained results is illustrated by numerical examples and simulations.