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

Starting from a symmetric state-feedback solution ensuring alpha-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.

Automated summary

In this paper, we propose a novel asymmetric scheduled extension method for preserving the original symmetric solution and extending the stability region to the union of all possible contractive ellipsoids. Our design is based on solving a parametric optimization problem, and we prove the Lipschitz properties of the resulting feedback law and compute its explicit state-feedback expression.