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Finite-time piecewise control for discrete-time stochastic nonlinear time-varying systems with time-varying delays

Author

Listed:
  • Liu, Jie
  • Chen, Guici
  • Wen, Shiping
  • Zhu, Song

Abstract

This study delves into the analysis and control of finite-time stochastic stability (FTSS) within discrete stochastic nonlinear time-varying systems (DSNTSs) with time-varying delays. Leveraging set-valued mappings and incorporating principles from differential inclusion theory, the DSNTSs are transformed into a set of differential inclusion subsystems, introducing a novel approach to system control. Sufficient conditions for FTSS are established through the introduction of discrete-time Lyapunov–Krasovskii functions and the application of linear matrix inequalities (LMIs). To ensure the FTSS of the systems, we introduce a set of piecewise state feedback controllers. In addition, we propose an optimized control algorithm founded on piecewise control, designed to enhance the overall cost-effectiveness. The efficacy of these methodological innovations is fully validated by a series of comprehensive numerical simulations.

Suggested Citation

  • Liu, Jie & Chen, Guici & Wen, Shiping & Zhu, Song, 2024. "Finite-time piecewise control for discrete-time stochastic nonlinear time-varying systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005344
    DOI: 10.1016/j.chaos.2024.114982
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