On one inner point algorithm for common Lyapunov functions

Abstract

In this paper, we consider the problem of existence and evaluation of common quadratic Lyapunov functions for a finite number of matrices. For this purpose, an inner point algorithm is proposed. The technique is based on Khalil (1982), where an algorithm is given which determines the diagonal stability of a matrix A. We obtain a necessary and sufficient condition for the existence and give an efficient algorithm which gives common solution in the case of existence and negative answer after a few iterations in the case of non existence. A number of examples are presented verifying the fast speed and efficiency of the obtained results. (c) 2022 Elsevier B.V. All rights reserved.