Global Exponential Stability Preservation Under Sampling and Approximated Delay-Dependent Feedbacks for Nonlinear Systems With Time-Varying Delays

• 成果类型: Article
• 署名作者: Caiazzo, Bianca; Leccese, Sara; Pepe, Pierdomenico; Petrillo, Alberto; Santini, Stefania
• 署名单位: University of Naples Federico II; University of L'Aquila
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3567250
• 发表日期: 2025
• 页码: 6984-6991
• 关键词: Delays; control theory; STABILITY; Nonlinear systems; Time-varying systems; State feedback; Splines (mathematics); germanium; system dynamics; Personal digital devices; Global exponential stability; globally Lipschitz time-delay systems; sampled-data stabilization; spline approximation; time-varying delays

摘要

This manuscript shows the global exponential stability preservation for the class of fully nonlinear retarded globally Lipschitz systems with time-varying delays under suitably fast sampling while considering at the same time the problem of the nonavailability in the buffer device of the system variables at some past (delayed) times. To this aim, a spline interpolation scheme is exploited to derive the digital control law, which has the benefit of ease of implementation. Main theoretical results are achieved by means of Halanay's inequality. The knowledge of a Lyapunov-Krasovskii functional is not required as long as the system at hand is globally exponentially stabilizable by a globally Lipschitz feedback in continuous time. Its knowledge is needed to quantify a maximum sampling period.