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This paper has investigated the finite-region stability and the dissipative control issue for two-dimensional (2D) Markov jump systems (MJSs) consisting of Fornasini-Marchesini (FM) model. By means of mathematical induction and Lyapunov functional, it reliably achieves sufficient conditions to guarantee that the system is finite-region stable (FRS) with the ( \(\mathcal {Q}\) , \(\mathcal {S}\) , \(\mathcal {R}\) )- \(\theta \) -dissipative performance. The solutions of the control scheme consists of the controller gain and dissipative performance \(\theta \) are solved by a set of linear matrix inequalities (LMIs). Finally, an example involving Darboux equations is employed to confirm the feasibility and effectiveness of the proposed approach.

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Finite-Region Dissipative Control 2D Markov Jump Systems: The FM Model Case

  • 会议论文

  • 发表日期：

    2025年

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  • Jiabao Wei,
  • Shuping He,
  • Chengcheng Ren

摘要

This paper has investigated the finite-region stability and the dissipative control issue for two-dimensional (2D) Markov jump systems (MJSs) consisting of Fornasini-Marchesini (FM) model. By means of mathematical induction and Lyapunov functional, it reliably achieves sufficient conditions to guarantee that the system is finite-region stable (FRS) with the ( \(\mathcal {Q}\) , \(\mathcal {S}\) , \(\mathcal {R}\) )- \(\theta \) -dissipative performance. The solutions of the control scheme consists of the controller gain and dissipative performance \(\theta \) are solved by a set of linear matrix inequalities (LMIs). Finally, an example involving Darboux equations is employed to confirm the feasibility and effectiveness of the proposed approach.