- Multidimensional systems
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By the term multidimensional systems or m-D systems we mean the branch of (mathematical) systems theory where not only one variable exists (like time), but several independent variables. Important problems like factorization and stability have recently attracted the interest of many researchers and practitioners.
The reason is that the factorization and stability of m-D systems (m > 1) is not a straightforward extension of the factorization and stability of 1-D systems because for example the fundamental theorem of algebra does not exist in the ring of m-D (m > 1) polynomials.
Applications
Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with many applications in biomedicine, X-ray technology and satellite communications. There are also some studies combining m-D systems with partial differential equations (PDEs).
References
- Tzafestas, S.G., ed (1986). Multidimensional Systems: Techniques and Applications. New York: Marcel-Dekker.
- Kaczorek, T. (1985). Two-Dimensional Linear Systems. Lecture Notes Contr. and Inform. Sciences. 68. Springer-Verlag.
- Bose, N.K., ed (1985). Multidimensional Systems Theory, Progress, Directions and Open Problems in Multidimensional Systems. Dordrecht, Holland: D. Reidel Publishing Company.
- Bose, N.K., ed (1979). Multidimensional Systems: Theory and Applications. IEEE Press.
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