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Minimal positive realizations: a survey of recent results and open problems

Luca Benvenuti, Lorenzo Farina (2003)

Kybernetika

In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of some examples, that the minimal dimension of a positive realization of a given transfer function, may be much “larger” than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions...

Modal operators on bounded residuated l -monoids

Jiří Rachůnek, Dana Šalounová (2008)

Mathematica Bohemica

Bounded residuated lattice ordered monoids ( R -monoids) form a class of algebras which contains the class of Heyting algebras, i.e. algebras of the propositional intuitionistic logic, as well as the classes of algebras of important propositional fuzzy logics such as pseudo MV -algebras (or, equivalently, GMV -algebras) and pseudo BL -algebras (and so, particularly, MV -algebras and BL -algebras). Modal operators on Heyting algebras were studied by Macnab (1981), on MV -algebras were studied by Harlenderová and...

Modal operators on MV-algebras

Magdalena Harlenderová, Jiří Rachůnek (2006)

Mathematica Bohemica

Modal operators on Heyting algebras were introduced by Macnab. In this paper we introduce analogously modal operators on MV-algebras and study their properties. Moreover, modal operators on certain derived structures are investigated.

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