## State-space realisations of linear 2-D systems with extensions to the general $$n$$D $$(n>2)$$ case.(English)Zbl 1007.93001

Lecture Notes in Control and Information Sciences. 263. Berlin: Springer. x, 232 p. (2001).
The topic of this book is to show how an algorithm developed by the author called “Elementary Operations Algorithm” (EOA) appears to be useful for obtaining state space realizations of 2D/$$n$$D linear systems. The author states that he reports on-going research and that many aspects of this problem are still open. After introductory sections and a presentation of mathematical prerequisites, the basic ingredient of the method is described: find the companion matrix of a bivariate polynomial. One then deals with systems with increasing complexity, from SISO to MIMO and from 1D, to 2D (mainly) and to $$n$$D. The $$n$$D case is not treated in depth (making the title inadequate); correspondingly, mainly numerical examples and applications are found. Minimality and nonsingularity of the realizations are not guaranteed using the proposed method.

### MSC:

 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory 93B15 Realizations from input-output data 93C35 Multivariable systems, multidimensional control systems 93B25 Algebraic methods 93B17 Transformations

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