A unified framework for the numerical solution of general quadratic matrix equations

Algebraic quadratic equations are special cases of a single generalized algebraic quadratic matrix equation (GQME). This paper focuses on the numerical solution of the GQME using probability-1 homotopy methods. A synoptic review of these methods and their application to algebraic matrix equations is provided as background. A large variety of analysis and design problems in systems and control are reported as special cases of the presented framework and some of them are illustrated via numerical examples from the literature.