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Asynchronous observer-based control for continuous-time singularly perturbed jump systems: A new Lyapunov function

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  • Wang, Dongji
  • Xu, Shengyuan

Abstract

The main focus of this paper centers around the asynchronous observer-based control of continuous-time jump systems with perturbation parameters via a hidden Markov model. In view of the difficulty in accurately obtaining the system state and system mode, an asynchronous controller under the framework of a hidden Markov model and observer is designed to stabilize the studied systems. Moreover, a kind of α-mode-dependent Lyapunov function that contains several common ones in the published works is constructed to analyze the system stability with the aid of Lyapunov stability theory, stochastic theory, etc. Subsequently, the gains of the observer-based asynchronous controller are obtained by solving matrix convex optimization problem. Finally, one case study is presented to verify the effectiveness and practicability of the established method under two different transition rate matrices of the hidden Markov model.

Suggested Citation

  • Wang, Dongji & Xu, Shengyuan, 2026. "Asynchronous observer-based control for continuous-time singularly perturbed jump systems: A new Lyapunov function," Applied Mathematics and Computation, Elsevier, vol. 527(C).
    • Handle: RePEc:eee:apmaco:v:527:y:2026:i:c:s009630032600127x
    DOI: 10.1016/j.amc.2026.130075
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