Estimation of asymptotic stability regions via composite homogeneous polynomial Lyapunov functions

Abstract

In this article, we present a new method to estimate the asymptotic stability regions for a class of nonlinear systems via composite homogeneous polynomial Lyapunov functions, where these nonlinear systems are approximated as a convex hull of some linear systems. Since level set of the composite homogeneous polynomial Lyapunov functions is a union set of several homogeneous polynomial functions, the composite homogeneous polynomial Lyapunov functions are nonconservative compared with quadratic or homogeneous polynomial Lyapunov functions. Numerical examples are used to illustrate the effectiveness of our method.

Keywords:

• invariant set
• asymptotic stability region
• homogeneous polynomial function
• composite Lyapunov function

Acknowledgements

The authors would like to express their appreciation to the associate editor and the anonymous reviewers whose constructive comments and suggestions were very helpful in improving the quality of this paper to its current standard.

Additional information

Funding

This work was supported by the Major Programme of National Natural Science Foundation of China [grant number 11190015]; National Natural Science Foundation of China [grant number 61374006]; Graduate Student Innovation Foundation of Jiangsu [grant number 3208004904].