Similarity transformations between two di erent minimal realizations of a given impulse response of a Discrete Event System are discussed. In the symmetrized max-algebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response and a minimal realization of the same impulse response in a standard form. It is conjectured that a...

A well-known result from linear system theory states that the minimal inner size of a factorization of the Hankel matrix H of a system gives the minimal order of a realization. In this brief it is shown that when dealing with positive linear systems, the existence of a factorization of the Hankel matrix into two nonnegative matrices is only a necessary condition for the existence of a positive ...

A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2dimensional surface.) We prove that if a minimal genus representation meets certain criteria then there is a minimal genus representa...

The paper deals with the realization theory of linear and bilinear hybrid systems, i.e. hybrid systems with continuous dynamics determined by linear ( respectively bilinear ) control systems. We will formulate necessary and sufficient conditions for the existence of a linear (bilinear ) hybrid system realizing the specified input/output maps. We will also present a characterization of a minimal...

In this paper, we propose a constructive realization procedure for 2D systems which may lead to a Fornasini-Marchesini local state-space model with much lower order than the existing realization procedure given by Bisiacco et al. Nontrivial examples are illustrated and the conditions for minimal realization are also discussed.

A circuit realization is presented for generalized one-multiplier lattice discrete two-dimensional (2-D) filters. The proposed structure has a minimun mumber of delay elements and multipliers. Based on this circuit realization, the corresponding state-space realization–representation is derived. The dimension of the 2-D state-space vector is minimal and the corresponding transfer function is ch...

The state realization is called minimal if it is either accessible and observable or its state dimension is minimal. In the linear case those two definitions are equivalent, but not for nonlinear time-invariant systems. It is shown that definitions remain equivalent in case one is searching for minimal realization in a larger class of nonlinear time-varying systems. First, nonlinear realization...

We consider interest rate models where the forward rates are allowed to be driven by a multidimensional Wiener process as well as by a marked point process. Assuming a deterministic volatility structure, and using ideas from systems and control theory, we investigate when the inputoutput map generated by such a model can be realized by a finite dimensional stochastic differential equation. We g...