Fixed-Time Input-to-State Stability for Singularly Perturbed Systems via Composite Lyapunov Functions

• 成果类型: Article
• 署名作者: Tang, Michael; Krstic, Miroslav; Poveda, Jorge I.
• 署名单位: University of California System; University of California San Diego; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3631559
• 发表日期: 2026
• 关键词: Stabilization; scales; perturbations; FRAMEWORK; seeking; DESIGN

摘要

We study singularly perturbed systems that exhibit input-to-state stability (ISS) with fixed-time properties in the presence of bounded disturbances. In these systems, solutions converge to the origin within a time frame independent of initial conditions when undisturbed, and to a vicinity of the origin when subjected to bounded disturbances. First, we extend the traditional composite Lyapunov method, commonly applied in singular perturbation theory to analyze asymptotic stability, to include fixed-time ISS. We demonstrate that if both the reduced system and the boundary layer system exhibit fixed-time ISS, and if certain interconnection conditions are met, then the entire multitime-scale system retains this fixed-time ISS characteristic, provided that the separation of time scales is sufficiently pronounced. Next, we illustrate our findings via analytical and numerical examples, including a novel application in fixed-time feedback optimization for dynamic plants with slowly varying cost functions.