This article demonstrates finite-time stability and control for nonlinear systems with state-dependent delays, suggesting improved management of uncertainties in real-time applications.
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.
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Elahe Moradi (2025) studied this question.
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