2004/03/26 by Christopher King, King, Christopher, Michael Nathanson +1
Engineering · Mathematics · #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations #math.OC
paper · pdf · doi:10.48550/arxiv.math/0403467
arxiv created 2004/03/26 · openalex publication_date 2004/03/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose that A and B are real stable matrices, and that their difference A-B is rank one. Then A and B have a common quadratic Lyapunov function if and only if the product AB has no real negative eigenvalue. This result is due to Shorten and Narendra, who showed that it follows as a consequence of the Kalman-Yacubovich-Popov solution of the Lur'e problem. Here we present a new and independent proof based on results from convex analysis and the theory of moments.