On Existence of Solutions to Structured Lyapunov Inequalities
Abstract
In this paper, we derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this algorithm can provide approximate solutions to optimisation programmes with constraints involving Lyapunov inequalities using linear or second order cone programming. This algorithm requires an initial feasible point, which we aim to provide in this paper. Our existence conditions are based on the so-called matrices. We also establish a link between matrices and an application of a small gain theorem to the drift matrix. We finally show how to construct these solutions in some cases without solving the full Lyapunov inequality.
Keywords
Cite
@article{arxiv.1603.07686,
title = {On Existence of Solutions to Structured Lyapunov Inequalities},
author = {Aviar Sootla and James Anderson},
journal= {arXiv preprint arXiv:1603.07686},
year = {2016}
}
Comments
To appear in the Proceedings of the 2016 American Control Conference