On maximal positive invariant set computation for rank-deficient linear systems
Systems and Control
2026-03-19 v1 Systems and Control
Optimization and Control
Abstract
The maximal positively invariant (MPI) set is obtained through a backward reachability procedure involving the iterative computation and intersection of predecessor sets under state and input constraints. However, standard static feedback synthesis may place some of the closed-loop eigenvalues at zero, leading to rank-deficient dynamics. This affects the MPI computation by inducing projections onto lower-dimensional subspaces during intermediate steps. By exploiting the Schur decomposition, we explicitly address this singular case and propose a robust algorithm that computes the MPI set in both polyhedral and constrained-zonotope representations.
Cite
@article{arxiv.2603.17686,
title = {On maximal positive invariant set computation for rank-deficient linear systems},
author = {Bogdan Gheorghe and Daniel Ioan and Cristian Flutur and Ionela Prodan and Florin Stoican},
journal= {arXiv preprint arXiv:2603.17686},
year = {2026}
}