Leveraging an LMI-Based Approach for Finite-Time Control of Nonlinear Systems in the Presence of State-Dependent Delays and Parametric Uncertainties

Elahe Moradi

Complexity, 2025, vol. 2025, 1-13

Abstract: In recent years, the study of finite-time stability (FTS) and finite-time control (FTC) of time-delay systems has attracted significant attention from researchers. This article investigates the problems of FTS and FTC for nonlinear systems in the presence of state-dependent delays and parametric uncertainties. The considered delay is time-varying, and the nonlinear system is assumed to satisfy the Lipschitz condition. First, sufficient conditions for ensuring FTS of the nonlinear time-delay system with parametric uncertainties are derived in the framework of linear matrix inequalities (LMIs). Next, LMI-based sufficient conditions are established for guaranteeing FTC via modified state-feedback control. The obtained FTS and FTC conditions are delay-dependent, providing a more precise characterization of the system’s transient behavior. To establish the theoretical results, the Newton–Leibniz formula and a Lyapunov–Krasovskii functional (LKF) candidate were employed. Finally, the effectiveness of the proposed approach is demonstrated through two illustrative examples and corresponding MATLAB simulations.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:6370708

DOI: 10.1155/cplx/6370708

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