Global Finite Time Stabilization of SISO Hurwitz Linear Systems Subject to Actuator Saturation: The Case of Real Eigenvalues

This paper considers the global finite time stabilization of linear systems subject to actuator saturation. We show that a controllable SISO system whose eigenvalues are real and negative can be globally stabilized in finite time by a homogeneous feedback law. To obviate numerical issues, this homogeneous feedback law is implemented by discretizing a compact set. Numerical simulation validates the effectiveness of the proposed approach.