{"ID":5551804,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-04T08:49:21.884923308Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00637","arxiv_id":"2607.00637","title":"Iterative graph lifting for automatic design of path-complete stability certificates","abstract":"Stability of switched linear systems under arbitrary switching is a fundamental problem in control theory, closely related to the joint spectral radius (JSR), which characterizes the worst-case growth rate of system trajectories. In this paper, we contribute to the path-complete approach for approximating the JSR. This framework constructs algebraic stability certificates using labeled directed graphs, known as path-complete graphs. These certificates can be computed via an associated optimization problem. We propose an iterative algorithm that refines path-complete graphs in an efficient and parsimonious manner. The algorithm relies on a graph-theoretic analysis of the optimality conditions of the underlying optimization problem. In particular, we derive a sufficient condition under which the exact JSR is attained by a given path-complete graph. When this condition is not satisfied, we identify bottleneck nodes by analyzing the graph induced by the active constraints. We then use this information to refine the path-complete graph via local graph lifting (node splitting), and repeat the procedure. Numerical experiments demonstrate the effectiveness and scalability of the proposed approach, outperforming state-of-the-art methods on all challenging instances tested.","short_abstract":"Stability of switched linear systems under arbitrary switching is a fundamental problem in control theory, closely related to the joint spectral radius (JSR), which characterizes the worst-case growth rate of system trajectories. In this paper, we contribute to the path-complete approach for approximating the JSR. This...","url_abs":"https://arxiv.org/abs/2607.00637","url_pdf":"https://arxiv.org/pdf/2607.00637v1","authors":"[\"Léa Ninite\",\"Raphaël M. Jungers\"]","published":"2026-07-01T08:51:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}