Simultaneous stabilization of polynomial nonlinear systems via density functions

This paper is concerned with simultaneous stabilization of a class of polynomial nonlinear systems with almost stability theory. The theory uses dual Lyapunov or density function criterion which has remarkable advantages over Lyapunov-based simultaneous stabilization. These advantages rely in convexity property of density functions. This property results in controller synthesis problems which are affine with respect to unknown polynomials variables. The results of almost stability are also extended to simultaneous asymptotic stability at the expense of adding some extra affine polynomial inequalities. Numerical method for verification of positivity of multivariate polynomials based on sum of square decomposition is used. Numerical examples and a fault tolerant design scheme are used to show the effectiveness of the proposed methods. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.