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For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in… (More)
We focus on erasure codes for distributed storage. The distributed storage setting imposes locality requirements because of easy repair demands on the decoder. We first establish the characterization of various locality properties in terms of the generator matrix of the code. These lead to bounds on locality and notions of optimality. We then examine the… (More)
In this paper, we consider linear shift-invariant discrete n-dimensional systems over Z in the behavioral context (nD behaviors) and investigate the regular implementation of autonomous behaviors with different degrees of autonomy. Taking into account that stable nD behaviors have the highest degree of autonomy, we apply the previous results to characterize… (More)
In this paper we study switched systems from a behavioral point of view. We define a switched behavioral system in terms of a bank of behaviors without referring to the notion of state. Moreover we give sufficient conditions for the stability of a switched behavior in terms of the behaviors in the underlying bank.
In this short paper we study the problem of finding necessary and sufficient conditions for regular implementability by partial interconnection for nD system behaviors. In  such conditions were obtained in the context of 1D systems. In the present paper we show that the conditions obtained in  are no longer valid in general in the nD context. We also… (More)
Two-dimensional convolutional codes are considered with code sequences having compact support indexed in N2 and taking values in Fn , where F is a finite field. Input-state-output representations of these codes are introduced and several aspects of such representations are discussed. Constructions of such codes with a designed distance are also presented.
Napp Avelli, D.a∗ Rapisarda, P. and Rocha, P. RD Unit Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal; ISIS group, University of Southampton, UK, e-mail: firstname.lastname@example.org; Department of Electrical and Computer Engineering, Faculty of Engineering, University of Oporto, Portugal, e-mail: email@example.com (Received 00… (More)
In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the… (More)
We consider autonomous n-dimensional systems over Zn with different degrees of autonomy, which are characterized by the freeness of the system projections on certain sub-lattices of Zn. The main purpose of this contribution is to investigate the implementation of such systems in the context of behavioral control. Taking into account that stable nD behaviors… (More)