2023/03/31 by Suad Krilašević, Krilašević, Suad, Sergio Grammatico +1
Engineering · Mathematics · #Differential Equations and Numerical Methods #FOS: Electrical engineering #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.18238
openalex publication_date 2023/03/31 · openalex created_date 2023/04/06 · openalex updated_date 2026/07/28
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems with jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set for small enough tuning parameters and sufficiently long time between almost all jumps. Second, under mild conditions on the jump mapping, we prove semi-global practical asymptotic stability of a restricted attractor set. Finally, for certain classes of dynamics, we prove semi-global practical asymptotic stability of the restricted attractor set for small enough tuning parameters and sufficiently long period between almost all jumps of the slow states only.