Multidim Syst Sign Process (2013) 24:51–64 DOI 10.1007/s11045-011-0154-3 Characterizations of global reachability of 2D structured systems Ricardo Pereira · Paula Rocha · Rita Simões Received: 9 February 2011 / Revised: 19 May 2011 / Accepted: 27 May 2011 / Published online: 12 June 2011 © Springer Science+Business Media, LLC 2011 Abstract The new concept of 2D structured system is defined and characterizations of global reachability are obtained. This paper extends well known results for the 1D case, according to which a structured system ( A λ , B λ ) is (generically) reachable if and only if its graph is spanned by a cactus, or, equivalently, if and only if the pair ( A λ , B λ ) is full generically row rank and irreducible. Keywords Structured system · 2D discrete system · Directed graphs · Global reachability 1 Introduction In 1974, Lin 1974 introduced the concept of structure for a linear time-invariant control system in order to model phenomena where the only available information is the existence or absence of relations between the relevant variables. In a structured system, the system matrices are supposed to have entries that are either zero or then assume arbitrary values, and each nonzero entry is identified with a parameter. In this setting, several system theoretic properties have been defined in a generic way, i.e., as holding for almost all the concretizations of the values of the parameters. This work was partially supported by FCT–Fundação para a Ciência e Tecnologia through CIDMA–Centro de Investigação e Desenvolvimento em Matemática e Aplicações of the University of Aveiro, Portugal. R. Pereira (B ) · R. Simões Department of Mathematics, University of Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal e-mail: ricardopereira@ua.pt R. Simões e-mail: ritasimoes@ua.pt P. Rocha Department of Electrical and Computer Engineering, Faculty of Engineering, University of Oporto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal e-mail: mprocha@fe.up.pt 123