Input-state-output representations of concatenated 2D convolutional codes

In this paper we investigate a novel model of concatenation of a pair of two-dimensional (2D) convolutional codes. We consider finite-support 2D convolutional codes and choose the so-called Fornasini-Marchesini input-state-output (ISO) model to represent these codes. More concretely, we interconnect in series two ISO representations of two 2D convolutional codes and derive the ISO representation of the ob- tained 2D convolutional code. We provide necessary condition for this representation to be minimal. Moreover, structural properties of modal reachability and modal observability of the resulting 2D convolutional codes are investigated

On the Connection Between the Stability of Multidimensional Positive Systems and the Stability of Switched Positive Systems

In this work, we study the connection of the stability of multidimensional positive systems with the stability of switched positive systems. In a previous work, we showed that the stability of a multidimensional positive system implies the stability of a related switched positive system. Here, we investigate the reciprocal implication

Dead beat observer synthesis

In the paper the observer design problem is investigated in the context of linear left shift invariant discrete behaviors, whose trajectories have support on the positive axis. Observability and reconstructibility properties of certain manifest variables from certain others, in the presence of latent variables, are defined and fully characterized. Necessary and sufficient conditions for the existence of either a dead-beat or an exact observer are introduced, and a complete parametrization of all dead-beat observers is given. (C) 1999 Elsevier Science B.V. All rights reserved

On the Common Linear Copositive Lyapunov Functions for Compartmental Switched Systems

For a positive switched system, the existence of a common linear copositive Lyapunov function (CLCLF) for the family of the subsystem matrices represents an important sufficient condition for its asymptotic stability. The main necessary and sufficient condition for the existence of a CLCLF (Fornasini and Valcher, IEEE Trans Autom Control 55:1933\u20131937, 2010, [1], Knorn et al, Automatica 45:1943\u20131947, 2009, [2]) consists in the explicit evaluation of the Hurwitz property of a family of matrices, where p is the number of subsystems and n the size of each subsystem. In this paper we show that, when restricting our attention to compartmental switched systems, the Hurwitz property may be checked on a smaller subset of smaller matrices. Based on this result, we provide an algorithm that allows to determine whether a CLCLF exists, by simply checking the column sums of matrix sets of increasingly lower dimension and cardinality

Identification of structured LTI MIMO state-space models

The identification of structured state-space model has been intensively studied for a long time but still has not been adequately addressed. The main challenge is that the involved estimation problem is a non-convex (or bilinear) optimization problem. This paper is devoted to developing an identificationmethod which aims to find the global optimal solution under mild computational burden. Key to the developed identification algorithm is to transform a bilinear estimation to a rank constrained optimization problem and further a difference of convex programming (DCP) problem. The initial conditionfor the DCP problem is obtained by solving its convex part of the optimization problem which happens to be a nuclear norm regularized optimization problem. Since the nuclear norm regularized optimization is the closest convex form of the low-rank constrained estimation problem, the obtained initialcondition is always of high quality which provides the DCP problem a good starting point. The DCP problem is then solved by the sequential convex programming method. Finally, numerical examples are included to show the effectiveness of the developed identification algorithm

An optimal control theory for systems defined over finite rings

this article we do formulate the problem in terms of linear systems theory and we show that the posed question is connected to some classical problems of systems theory. A convolutional code can be viewed as a discrete time linear system defined over a finite field F and we will say more about it in Section 2. Sometimes it is too restrictive to work over a finite field F and because of this several authors did recently consider codes over a finite ring R (such as the ring Z