# Fornasini Marchesini Teoria Dei Sistemi 20

## Fornasini Marchesini Teoria Dei Sistemi 20

What is the Fornasini Marchesini theory of systems 20? It is a mathematical framework for modeling and analyzing two-dimensional dynamical systems, also known as 2D systems or doubly-indexed systems. These are systems whose state and input variables depend on two independent discrete indices, such as space and time, or row and column. Examples of 2D systems include digital image processing, cellular automata, distributed parameter systems, and ecological networks.

The Fornasini Marchesini theory of systems 20 was developed by Ettore Fornasini and Giuseppe Marchesini, two professors of electrical engineering at the University of Padova, Italy. They published their seminal papers on this topic in the late 1970s and early 1980s , and later wrote a book on the subject. Their theory provides a state-space representation of 2D systems that generalizes the classical one-dimensional (1D) theory of linear systems. It also introduces algebraic criteria for testing structural properties such as reachability, observability, stability, and minimality.

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The Fornasini Marchesini theory of systems 20 has been widely recognized as a fundamental contribution to the field of multidimensional systems theory. It has inspired many subsequent research works on various aspects of 2D systems, such as realization, control, filtering, identification, robustness, and positivity. It has also found applications in various domains, such as signal processing, robotics, cryptography, and biology. The Fornasini Marchesini theory of systems 20 is still an active area of research today, with new developments and challenges emerging from the increasing complexity and interconnection of modern 2D systems.

## References

E. Fornasini and G. Marchesini, "Doubly-indexed dynamical systems: state-space models and structural properties", Math. Systems Theory 12 (1978), pp. 59-72.

E. Fornasini and G. Marchesini, "State-space realization theory of two-dimensional filters", IEEE Trans. Automat. Control AC-25 (1980), pp. 910-917.

E. Fornasini and G. Marchesini, "One-sided and two-sided linear 2-D system theory: a unified approach", Multidimens. Syst. Signal Process. 1 (1990), pp. 329-354.

E. Fornasini and G. Marchesini, "2D Linear Systems", Springer-Verlag Berlin Heidelberg (2016).

A survey of recent advances in 2D systems theory can be found in: M.K.Sain et al., "Multidimensional Systems Theory: Progress, Directions and Open Problems in Multidimensional Systems", Springer-Verlag Berlin Heidelberg (2017).

Some examples of applications of 2D systems theory can be found in: A.G.Constantinides et al., "Two-Dimensional Signal and Image Processing", Prentice Hall (1990); R.J.Plemmons et al., "Two-Dimensional Systems: From Introduction to State-of-the-Art", Springer-Verlag Berlin Heidelberg (2016); A.Bacciotti et al., "Positive Systems: Theory and Applications", Springer-Verlag Berlin Heidelberg (2017).