A generalized minimal partial realization problem

Minimal stable partial realization

An asymptotically stable minimal order realization of a partial sequence of Markov parameters is achieved by reducing the problem to a standard but minimal one in decision algebra. Summary—In this paper two equivalent sets of necessary and sufficient conditions for the existence of an asymptotically stable partial realization are developed. Both sets are expressed as multivariable polynomial eq...

Minimal partial realization from generalized orthonormal basis function expansions

A solution is presented for the problem of realizing a discrete-time LTI state-space model of minimal McMillan degree such that its :rst N expansion coe;cients in terms of generalized orthonormal basis match a given sequence. The basis considered, also known as the Hambo basis, can be viewed as a generalization of the more familiar Laguerre and two-parameter Kautz constructions, allowing genera...

On the partial realization problem

We consider here a two sided interpolation problem where we want to minimize the degree of the interpolant. We show that this degree is given by the rank of a particular solution to a Sylvester equation which, in some particular cases becomes a Löwner or a Hankel matrix. We consider an application to the usual partial realization problem. The results are quite general and no particular assumpti...

A matrix Euclidean algorithm for minimal partial realization

On minimal realization of IF-languages: A categorical approach

he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and ...