Structural Stability of Boundary Equilibria in a class of hybrid systems: Analysis and Use for Control System Design

This paper is concerned with the structural stability of boundary equilibria in a class of hybrid systems, that of piecewise linear continuous systems. Specifically, we study the structural stability under parameter variations of equilibria lying on discontinuity boundaries in phase space dividing regions where the system under investigation is smooth. We show that it is possible to give a set of conditions to account for the possible dynamical scenarios that can be observed. We present a novel scenario where under perturbations, the equilibrium of interest does not persist and a family of stable limit cycles is generated with amplitudes increasing linearly under parameter perturbations. We propose a novel switching control strategy based on the use of the results presented in the paper.