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The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates

Author

Listed:
  • WonIl Lee

    (School of Electronic Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of Korea)

  • JaeWook Shin

    (School of Electronic Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of Korea)

  • BumYong Park

    (Department of IT Convergence Engineering, Kumoh National Institute of Technology, Gumi-si 39177, Republic of Korea)

Abstract

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller.

Suggested Citation

  • WonIl Lee & JaeWook Shin & BumYong Park, 2024. "The Strictly Dissipative Condition of Continuous-Time Markovian Jump Systems with Uncertain Transition Rates," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:639-:d:1343290
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    References listed on IDEAS

    as
    1. Yonit Barron, 2023. "Integrating Replenishment Policy and Maintenance Services in a Stochastic Inventory System with Bilateral Movements," Mathematics, MDPI, vol. 11(4), pages 1-35, February.
    2. N. Anbazhagan & Gyanendra Prasad Joshi & R. Suganya & S. Amutha & V. Vinitha & Bhanu Shrestha, 2022. "Queueing-Inventory System for Two Commodities with Optional Demands of Customers and MAP Arrivals," Mathematics, MDPI, vol. 10(11), pages 1-12, May.
    3. P. Shi & E. K. Boukas, 1997. "H ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 75-99, October.
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