2013/03/11 by Şerban Sabău, Cristian Oarâ, Sabau, Serban +5
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Advanced Control Systems Optimization #FOS: Mathematics #Gene Regulatory Network Analysis #Neural Networks and Applications #Nonlinear Dynamics and Pattern Formation #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.1303.2760
openalex publication_date 2013/03/11 · openalex created_date 2022/08/30 · openalex updated_date 2026/07/28
In this paper we study state-space realizations of Linear and Time-Invariant\n(LTI) systems. Motivated by biochemical reaction networks, Gon ccalves and\nWarnick have recently introduced the notion of a em Dynamical Structure\nFunctions (DSF), a particular factorization of the system's transfer function\nmatrix that elucidates the interconnection structure in dependencies between\nmanifest variables. We build onto this work by showing an intrinsic connection\nbetween a DSF and certain sparse left coprime factorizations. By establishing\nthis link, we provide an interesting systems theoretic interpretation of\nsparsity patterns of coprime factors. In particular we show how the sparsity of\nthese coprime factors allows for a given LTI system to be implemented as a\nnetwork of LTI sub-systems. We examine possible applications in distributed\ncontrol such as the design of a LTI controller that can be implemented over a\nnetwork with a pre-specified topology.\n