This paper presents new results about the optimization based generation of chemical reaction networks (CRNs) of higher deficiency. Firstly, it is shown that the graph structure of the realization containing the maximal number of reactions is unique if the set of possible complexes is fixed. Secondly, a mixed integer programming based numerical procedure is given for computing a realization cont...

Given a proper antistable rational transfer function g, a balanced realization of g is constructed as a matrix representation of the abstract shift realization introduced by Fuhrmann (1976). The required basis is constructed as a union of sets of polynomials orthogonal with respect to weights given by the squares of the absolute values of minimal degree Schmidt vectors of the corresponding Hank...

We address the partial realization problem for linear descriptor systems. A general solution to this problem using the Markov parameters of the system defined via its Laurent series is provided. For proper descriptor systems, we also discuss a numerically feasible algorithm for computing a partial minimal realization based on the unsymmetric Lanczos process. Applications to model reduction for ...

Minimal valid automata (MVA) refer to valid automata models that fit a given input-output sequence sample from a Mealy machine model. They are minimal in the sense that the number of states in these automata is minimal. Critical to system identification problems of discrete event systems, MVA can be considered as a special case of the minimization problem for incompletely specified sequential m...

There has been much interest in modeling open quantum linear passive systems as a fundamental class of quantum control systems. Quantum linear passive systems are parameterized by triple G ∼ (S,C,Ω) consisting of an input-to-output scattering matrix S, an input-system coupling matrix C, a Hamiltonian matrix Ω for normal modes. The purpose of this paper is to characterize these systems using rec...

In this paper we discuss some recent advances in modeling and identiication of stationary processes. We point out that identiication of linear state-space models for stationary signals can be seen as stochastic realization of wide-sense stationary processes in an appropriate background Hilbert space. The geometric theory of stochastic realization developed in the last two decades plays an impor...

The paper represents the first part of a series of papers on realization theory of switched systems. Part I presents realization theory of linear switched systems, Part II presents realization theory of bilinear switched systems. More precisely, in Part I necessary and sufficient conditions are formulated for a family of input-output maps to be realizable by a linear switched system and a chara...

In this paper we extend Kalman's concept of partial realization and deene generalized partial realizations of nite matrix sequences by descriptor systems. Our deenition is in agreement with the realization theory for deterministic boundary value descriptor systems 15]. The aim of this contribution is to prove a counterpart of Kalman's main theorem of realization theory for generalized partial r...