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Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition

Xinye Guo1, Yan Li2, Xikui Liu1,3

  • 1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China.

Entropy (Basel, Switzerland)
|April 26, 2024
PubMed
Summary

This study develops finite-time H∞ controllers for stochastic systems with time-delay and unknown probabilities. The methods ensure system boundedness and H∞ performance, validated by examples.

Keywords:
H∞ controlMarkovian jump systemsdiscrete-time systemsfinite-time controlpartly unknown transition probabilities

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Area of Science:

  • Control Theory
  • Systems Engineering
  • Stochastic Systems

Background:

  • Stochastic discrete-time Markovian jump systems are complex due to time-delays and uncertain transition probabilities.
  • Finite-time control is crucial for systems requiring rapid response and guaranteed performance bounds.

Purpose of the Study:

  • To design finite-time H∞ controllers for stochastic discrete-time Markovian jump systems with time-delay and partly unknown transition probabilities.
  • To ensure the closed-loop systems achieve finite-time boundedness and finite-time H∞ boundedness.

Main Methods:

  • Construction of stochastic finite-time (SFT) H∞ state feedback controllers and observer-based controllers.
  • Application of the Lyapunov-Krasovskii functional (LKF) method to derive stability conditions.
  • Utilization of the linear matrix inequality (LMI) approach for controller gain computation.

Main Results:

  • Sufficient conditions for SFT boundedness and SFT H∞ boundedness of the closed-loop systems are established.
  • Controller gains are derived using the LMI approach.
  • Numerical examples demonstrate the effectiveness of the proposed control schemes.

Conclusions:

  • The proposed controller design schemes effectively address the finite-time H∞ control problem for the targeted stochastic systems.
  • The LKF and LMI methods provide a robust framework for achieving desired system performance and stability.