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<p>This paper provides a comprehensive investigation into the finite-time guaranteed cost control (FTGCC) problem for Caputo tempered nonlinear fractional-order systems with time delays. The proposed method ensures finite-time stability while establishing an upper bound on a predefined quadratic cost function. It effectively tackles the challenges arising from bounded memory, finite lifespans, uncertainties, and time delays. The main contributions of this work are: (1) extending the analysis of FTGCC to Caputo tempered fractional-order systems with time delays, (2) proposing a novel lemma for the Caputo tempered fractional derivative of quadratic functions, facilitating the use of general quadratic Lyapunov functions in stability analysis, and (3) deriving delay-dependent sufficient conditions for guaranteed cost state-feedback control, formulated as linear matrix inequalities (LMIs) that can be efficiently solved using computational tools. The feasibility and effectiveness of the proposed approach are demonstrated through two simulation examples.</p>

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Finite-time guaranteed cost control for tempered nonlinear fractional-order systems with delays: a novel stability approach

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Tran Ngoc Tuan,
  • Mai Viet Thuan,
  • Nguyen Truong Thanh

摘要

This paper provides a comprehensive investigation into the finite-time guaranteed cost control (FTGCC) problem for Caputo tempered nonlinear fractional-order systems with time delays. The proposed method ensures finite-time stability while establishing an upper bound on a predefined quadratic cost function. It effectively tackles the challenges arising from bounded memory, finite lifespans, uncertainties, and time delays. The main contributions of this work are: (1) extending the analysis of FTGCC to Caputo tempered fractional-order systems with time delays, (2) proposing a novel lemma for the Caputo tempered fractional derivative of quadratic functions, facilitating the use of general quadratic Lyapunov functions in stability analysis, and (3) deriving delay-dependent sufficient conditions for guaranteed cost state-feedback control, formulated as linear matrix inequalities (LMIs) that can be efficiently solved using computational tools. The feasibility and effectiveness of the proposed approach are demonstrated through two simulation examples.