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<p>This study investigates the implementation of sampled-data control techniques in positive Markov jump systems (PMJSs), aiming to ensure exponential stability in the mean and a predefined <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathscr {L}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-gain performance. Initially, we develop a sampled-data model for PMJSs and examine its mean stability characteristics. Subsequently, sufficient criteria are derived to guarantee that the system achieves the targeted <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathscr {L}_1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">L</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-gain performance, with particular emphasis on how the sampling period influences system dynamics. These criteria are utilized to formulate a sampled-data controller, with its gains determined using a linear programming method. The proposed methodology’s effectiveness is confirmed through numerical simulations, which support the theoretical results.</p>

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\(\mathscr {L}_1\)-Gain stability analysis for markov jump sampled-data control systems via co-positive-type LKF approach

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • R. Suresh,
  • G. Devi,
  • R. Vadivel,
  • Nallappan Gunasekaran

摘要

This study investigates the implementation of sampled-data control techniques in positive Markov jump systems (PMJSs), aiming to ensure exponential stability in the mean and a predefined \(\mathscr {L}_1\) L 1 -gain performance. Initially, we develop a sampled-data model for PMJSs and examine its mean stability characteristics. Subsequently, sufficient criteria are derived to guarantee that the system achieves the targeted \(\mathscr {L}_1\) L 1 -gain performance, with particular emphasis on how the sampling period influences system dynamics. These criteria are utilized to formulate a sampled-data controller, with its gains determined using a linear programming method. The proposed methodology’s effectiveness is confirmed through numerical simulations, which support the theoretical results.