Lyapunov function gradient generated robust control in the absence of the nominal stabilizing control

Abstract

A relevant facet of the application of Lyapunov gradient-generated robust control to unstable linear autonomous plants is explored. It is demonstrated that if the plant, the output, and the nominal stabilizing control satisfy certain conditions, then the robust component alone stabilizes the nominal plant. An example characterized by two zero eigenvalues and two negative real value poles is presented. These results assure that the robust component will fulfill the role of nominal stabilization successfully so long as the possible magnitude of the robust component can overcome the contribution of the instability to positiveness of the Lyapunov rate.