The Constrained Lyapunov Problem Applied to the Case of a Linear Plant with an Ad Hoc Linear Output Feedback Nominal Stabilizing Controller

Abstract

Given a stabilizing linear output feedback control for a given linear system, we show how to determine if the candidate control is consistent with the constrained Lyapunov problem; i.e., the chosen output feedback can be obtained by the proper choice of a Lyapunov function for the stabilized system. Necessary and sufficient conditions are stated, a solution procedure is developed, and an illustrative example is provided.