Sensitivity to perturbations in variable structure systems

摘要

Variable structure systems are systems for which the behaviour switches between several configurations, each of them modelled by a system of ODEs. The behaviour of perturbations around trajectories of variable structure systems is studied and a sensitivity formula is derived. This formula consists of a chain of monodromy matrices and corrections which are rank-1 updates of the unity matrix. Applications include the adaptation of classical shooting algorithms for computing periodic solutions to piecewise smooth systems.