Scholarlink

<p>This paper develops a robust framework for stability analysis of uncertain two-dimensional discrete-time systems with time-varying delays and generalized overflow arithmetic. The systems are represented in the Fornasini–Marchesini second local state-space form with polytopic parameter uncertainties. A convex stability condition is derived for uncertain systems, and an additional condition is provided for the case without uncertainties. The analysis relies on a tailored Lyapunov–Krasovskii functional with relaxed positive definiteness requirements, combined with Jensen–Wirtinger and reciprocally convex summation techniques to address delay-dependent terms. Furthermore, an extended lemma, adapted from the one-dimensional case, is introduced to characterize the interaction between system states and nonlinearities induced by overflow. The resulting stability conditions are expressed as linear matrix inequalities, ensuring computational tractability. Numerical examples demonstrate that the proposed method achieves larger admissible delay bounds compared with existing approaches, thereby improving stability assessment of two-dimensional discrete-time systems with delays and overflow effects.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Robust Delay-Dependent Stability of Uncertain 2-D Discrete-Time Systems with Generalized Overflow Arithmetic

  • 期刊论文

  • 发表日期：

    2026年4月13日

查看全文
  • Nabil Echakroune,
  • El Houssaine Tissir,
  • Abdelaziz Hmamed

摘要

This paper develops a robust framework for stability analysis of uncertain two-dimensional discrete-time systems with time-varying delays and generalized overflow arithmetic. The systems are represented in the Fornasini–Marchesini second local state-space form with polytopic parameter uncertainties. A convex stability condition is derived for uncertain systems, and an additional condition is provided for the case without uncertainties. The analysis relies on a tailored Lyapunov–Krasovskii functional with relaxed positive definiteness requirements, combined with Jensen–Wirtinger and reciprocally convex summation techniques to address delay-dependent terms. Furthermore, an extended lemma, adapted from the one-dimensional case, is introduced to characterize the interaction between system states and nonlinearities induced by overflow. The resulting stability conditions are expressed as linear matrix inequalities, ensuring computational tractability. Numerical examples demonstrate that the proposed method achieves larger admissible delay bounds compared with existing approaches, thereby improving stability assessment of two-dimensional discrete-time systems with delays and overflow effects.