{"ID":2893466,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13000","arxiv_id":"2507.13000","title":"Geometric Stability Analysis for Differential Inclusions Governed by Maximally Monotone Operators","abstract":"This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a normal cone. However, the resulting dynamics are often difficult to analyze directly due to the absence of Lipschitz selections and boundedness. To overcome these challenges, we introduce a regularized system based on a fixed Lipschitz approximation of the convexified mapping. From this approximation, we extract a single-valued Lipschitz selection that preserves the essential geometric features of the original system. This framework enables the application of nonsmooth Lyapunov methods and Hamiltonian-based stability criteria. Instead of approximating trajectories, we focus on analyzing a simplified system that faithfully reflects the structure of the original dynamics. Several examples are provided to illustrate the method's practicality and scope.","short_abstract":"This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a normal cone. However, the resulting dynamics are often difficult to analyze dire...","url_abs":"https://arxiv.org/abs/2507.13000","url_pdf":"https://arxiv.org/pdf/2507.13000v1","authors":"[\"Hassan Saoud\",\"Michel Théra\",\"Minh N. Dao\"]","published":"2025-07-17T11:16:50Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}