It is a well-know fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive s...

The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown that there exists a positive (minimal) realization of an improper transfer function T (z) = n(z)/d(z) if the coeffici...

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. We consider a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the max-plus-algebraic zero element or to the maxplus-algebrai...

One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. We consider a simpliied version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the max-plus-algebraic zero element or to the max-plus-algebrai...

In this paper we address the problem of computing a minimal state-space realization from partial knowledge of an expansion in terms of generalized rational orthogonal basis functions. The basis functions considered are generated by stable all-pass £lters. It is shown how a minimal state-space realization can be found on the basis of complete knowledge of the expansion coef£cients. Subsequently ...

The context of this article is the program to develop monoidal bicategories with a feedback operation as an algebra of processes with applications to concurrency theory The objective here is to study reachability minimization and minimal realization in these bicategories In this set ting the automata are cells in contrast with previous studies where they appeared as objects As a consequence we ...

We show that the minimal dimension of a linear realization over the (max,+) semiring of a convex sequence is equal to the minimal size of a decomposition of the sequence as a supremum of discrete affine maps. The minimal-dimensional realization of any convex realizable sequence can thus be found in linear time. The result is based on a bound in terms of minors of the Hankel matrix.