2025/12/24 by Michael Tang, Miroslav Krstic, Tang, Michael +3
Engineering · #Adaptive Control of Nonlinear Systems #Extremum Seeking Control Systems #FOS: Electrical engineering #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2512.21314
openalex publication_date 2025/12/24 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
We develop a Lyapunov-based small-gain theorem for establishing fixed-time input-to-state stability (FxT-ISS) guarantees in interconnected nonlinear dynamical systems. The proposed framework considers interconnections in which each subsystem admits a FxT-ISS Lyapunov function, providing robustness with respect to external inputs. We show that, under an appropriate nonlinear small-gain condition, the overall interconnected system inherits the FxT-ISS property. In this sense, the proposed result complements existing Lyapunov-based smallgain theorems for asymptotic and finite-time stability, and enables a systematic analysis of interconnection structures exhibiting fixed-time stability. To illustrate the applicability of the theory, we study feedback-based optimization problems with time-varying cost functions, and Nash-equilibrium seeking for noncooperative games with nonlinear dynamical plants in the loop. For both problems, we present a class of non-smooth gradient or pseudogradient-based controllers that achieve fixed-time convergence without requiring time-scale separation and using real-time feedback. Numerical examples are provided to validate the theoretical findings.