An Asymmetric Stabilizer Based on Scheduling Shifted Coordinates for Single-Input Linear Systems with Asymmetric Saturation

Abstract

Starting from a symmetric state-feedback solution ensuring α-exponential
convergence in an ellipsoidal sublevel set, with asymmetric saturation
and single-input linear plants, we propose a novel asymmetric scheduled
extension preserving the original symmetric solution in that sublevel
set and extending the guaranteed stability region to the union of all
possible contractive ellipsoids centered at a shifted equilibrium. Our
design being based on the solution of a parametric optimization problem,
we prove Lipschitz properties of the ensuing feedback law and we
compute its explicit state-feedback expression.