Decentralized prescribed-time input-to-state stabilization for interconnected normal form nonlinear systems

Thus far, decentralized prescribed-time regulation of interconnected nonlinear systems with unknown control coefficients and persistent disturbances has remained unresolved, despite the prevalence of such scenarios in practical applications. This paper provides a systematic solution by integrating state-scaling-based time-varying feedback with a low-conservatism design framework. The stability analysis includes a comprehensive examination of the interconnection dynamics across subsystems, followed by a small-gain analysis for input-to-state stable (ISS) cascade systems. We rigorously prove that the proposed decentralized controllers can achieve global stabilization of the interconnected system within a user-defined time, without requiring prior knowledge of interconnected strengths. A key technical lemma is established, enabling the demonstration that the designed control strategy is robust against persistent disturbances and interconnected uncertainties while also facilitating the derivation of a relaxed condition for the small-gain theorem. The effectiveness of the proposed framework is validated using numerical simulations and a practical case study on room temperature regulation, with results confirming both theoretical guarantees and practical applicability.