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Abstract: In this paper we consider discrete-time positive switched systems, switching among autonomous subsystems, characterized either by monomial matrices or by circulant matrices. Necessary and sufficient conditions are provided guaranteeing either (global uniform) asymptotic stability or stabilizability (i.e. the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence). Such conditions lead to simple algorithms that allow to easily detect, under suitable conditions, whether a given positive switched system is not stabilizable. [Copyright &y& Elsevier]

Abstract: Reachability and observability of two-dimensional (2D) discrete state-space models are introduced in two different forms: a local form, which refers to single local states, and a global form, which pertains to the infinite set of local states lying on a separation set [M. Bisiacco, State and output feedback stabilizability of 2D systems, IEEE Trans. Circ. Syst., CAS-32 (1985) 1246–1249; E. Fornasini, G. Marchesini, Global properties and duality in 2-D systems, Syst. Control Lett. 2 (1) (1982) 30–38]. While local reachability and observability can be naturally characterized by resorting to classical state space techniques, their global counterparts are better addressed by means of polynomial techniques. In this paper, reachability and observability are introduced in the context of 2D positive systems and their global versions investigated via a polynomial approach. Necessary and sufficient conditions for the existence of these properties are provided and, in particular, polynomial canonical forms for globally reachable/observable positive systems with scalar inputs/scalar outputs are provided. [Copyright &y& Elsevier]

In this paper, polynomial matrix fraction descriptions (MFDs) are used as a tool for investigating the structure of a (linear) convolutional code and the family of its encoders and syndrome formers. As static feedback and precompensation allow to obtain all minimal encoders (in particular, polynomial encoders and decoupled encoders) of a given code, a simple parametrization of their MFDs is provided. All minimal syndrome formers, by a duality argument, are obtained by resorting to output injection and postcompensation. Decoupled encoders are finally discussed as well as the possibility of representing a convolutional code as a direct sum of smaller ones. [Copyright &y& Elsevier]