This letter develops certificates that propagate compatibility of multiple control barrier function (CBF) constraints from sampled vertices to their convex hull. Under mild concavity and affinity assumptions, we present three sufficient feasibility conditions under which feasible inputs over the convex hull can be obtained per coordinate, with a common input, or via convex blending. We also describe the associated computational methods, based on interval intersections or an offline linear program (LP). Beyond certifying compatibility, we give conditions under which the quadratic-program (QP) safety filter is affine in the state. This enables explicit implementations via convex combinations of vertex-feasible inputs. Case studies illustrate the results.
", "doi": "10.1109/lcsys.2025.3648436", "issn": "2475-1456", "publisher": "IEEE", "publication": "IEEE Control Systems Letters", "publication_date": "2025-12-25", "volume": "9", "pages": "3011 - 3016" }, { "id": "authors:wymkb-5r645", "collection": "authors", "collection_id": "wymkb-5r645", "cite_using_url": "https://authors.library.caltech.edu/records/wymkb-5r645", "type": "article", "title": "Modal Strong Structural Controllability: Graph-Based Analysis in LTI Systems", "author": [ { "family_name": "Mousavi", "given_name": "Shima Sadat", "orcid": "0000-0002-6932-3073", "clpid": "Mousavi-Shima-Sadat" } ], "abstract": "This paper introduces a new concept of modal strong structural controllability in linear time-invariant (LTI) systems. An eigenvalue of a system matrix is considered controllable if it can be directly influenced by the control inputs. We focus on an arbitrary set Δ⊆C and define a specific family of systems as modal strongly structurally controllable with respect to Δ if, for all systems in this family, every λ∈Δ is a controllable eigenvalue. In this family of LTI systems, the zero/nonzero/arbitrary pattern of system matrices is known, along with additional information about the spectrum of the subsystems, derived from their physical properties. To establish controllability conditions, we define a Δ-graph and use a coloring process to relate the set of control subsystems to zero forcing sets. We define efficient Δ, and for networks of one-dimensional subsystems, we prove that the graph-theoretic condition is both necessary and sufficient when Δ is efficient. Moreover, for cases where Δ is not efficient, we establish conditions under which it can be partitioned into efficient subsets. Furthermore, we demonstrate how our approach can derive existing results on strong structural controllability when Δ={0} or Δ=C\u2216{0}.
", "doi": "10.1109/tac.2025.3568561", "issn": "0018-9286", "publisher": "IEEE", "publication": "IEEE Transactions on Automatic Control", "publication_date": "2025-05-09", "pages": "1-14" } ]