On the equilibrium sets of linear systems with saturating feedback control

A linear system under the action of saturating feedback control (SFC) behaves as a nonlinear dynamical system. This raises the possibility of the existence of more than one equilibrium point. The problem of the existence of equilibrium points as a prerequisite to study the region of attraction for linear systems with SFC is addressed. Most results are derived from the fact that the topological degree of the open-loop system is invariant under SFC. The equilibrium set structure for one-input systems is completely characterized