2020/07/18 by Robert L. Grossman, Grossman, Robert L., Richard G. Larson +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #05C05 (Secondary) #93B15 (Primary) 16T10 #93C10 #Advanced Control Systems Optimization #Dynamical Systems (math.DS) #FOS: Mathematics #Formal Methods in Verification #Gene Regulatory Network Analysis #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2007.09526
openalex publication_date 2020/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use the theory of bialgebras to provide the algebraic background for state space realization theorems for input-output maps of control systems. This allows us to consider from a common viewpoint classical results about formal state space realizations of nonlinear systems and more recent results involving analysis related to families of trees. If H is a bialgebra, we say that p ∈ H^* is differentially produced by the algebra R with the augmentation ε if there is right H-module algebra structure on R and there exists f ∈ R satisfying p(h) = ε(f ⋅ h). We characterize those p ∈ H^* which are differentially produced.