MAT Tesis doctorado

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Contributions to the singular perturbation theory of infinite-dimensional coupled systems
(2025) Arias Neira, Gonzalo Andrés; Cerpa, Eduardo; Marx, Swann; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
Singular perturbation and separation of time scales methods have been used to study the stability and control design for coupled ODE systems with different time scales for many years. This important literature was motivated by the fact that systems with significantly different time scales appear in several applications, in which the constituents of a coupled system may model different physical phenomena taking place in different time scales. The singular perturbation method (SPM), roughly speaking, aims to decouple a full system into two approximated subsystems based on a suitable time-scale separation. This thesis addresses problems concerning the stability, Tikhonov's approximation, stabilization, and control of singularly perturbed coupled infinite-dimensional systems.