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Finite-time stability and stabilization for highly nonlinear stochastic Markov jump systems
1The College of Intelligent Manufacturing and Control Engineering, Shandong Institute of Petroleum and Chemical Technology, Dongying 257061, PR China.
ISA Transactions
|March 25, 2025
Summary
This study addresses finite-time stability (FTS) for highly nonlinear stochastic Markov jump systems (HNSMJSs). It introduces new criteria and an asynchronous controller for mth moment finite-time stabilization (m-MFT stabilization), extending results to time-varying delays.
Area of Science:
- Control theory
- Stochastic systems
- Nonlinear dynamics
Background:
- Finite-time stability (FTS) research primarily targets linear and nonlinear systems, with limited studies on highly nonlinear systems.
- Existing FTS methods, often using Lyapunov functions, impose restrictive constraints on Lyapunov function features and diffusion operators across system modes.
- This limits the flexibility in selecting appropriate Lyapunov functions for complex systems.
Purpose of the Study:
- To investigate finite-time stability (FTS) and asynchronous control for highly nonlinear stochastic Markov jump systems (HNSMJSs).
- To develop less restrictive criteria for mth moment finite-time stability (m-MFTS) and design an asynchronous controller for mth moment finite-time stabilization (m-MFT stabilization).
- To generalize existing results by extending analyses from deterministic time delays to time-varying delays in HNSMJSs.
Main Methods:
- Development of novel criteria for mth moment finite-time stability (m-MFTS) in both Lyapunov function and parameter forms.
- Design of an asynchronous controller to achieve mth moment finite-time stabilization (m-MFT stabilization) for HNSMJSs.
- Extension of stability analysis to systems with time-varying delays, providing more generalized results.
Main Results:
- The study presents new criteria for mth moment finite-time stability (m-MFTS) applicable to highly nonlinear stochastic Markov jump systems (HNSMJSs).
- An effective asynchronous controller is proposed to ensure mth moment finite-time stabilization (m-MFT stabilization).
- The research extends stability analysis to HNSMJSs with time-varying delays, offering a more comprehensive framework.
Conclusions:
- The developed criteria and asynchronous control strategy effectively address finite-time stability challenges in highly nonlinear stochastic systems.
- The proposed methods relax previous restrictive conditions on Lyapunov functions and diffusion operators.
- The generalization to time-varying delays enhances the applicability and robustness of the findings for HNSMJSs.
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