# Two-Dimensional Linear Systems by Tadeusz Kaczorek (eds.)

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Extra resources for Two-Dimensional Linear Systems

Example text

2/ is called the transfer function matrix of the system. The transfer function matrix gives an external description of the syst tem. 2/. 41 45 where xhlzl,z2/, xV/zl,z2/, xhlo,z2/, XVlz1,0/, UlZq,Z2/ and Ylzl,z2/ are the 2-D Z transforms of xh/i,~/, xV/i,j/, xh/o,j/, xV/i,O/, u/i,j/ and y/i,j/, respectively. 61 In2Z2 and Ik is the identity matrix of order k. ol D is the transfer function matrix of RM. 1 Mertzios-Paraskevopoulos" Formula. 1 [10] The transfer function matrix C/zl,z2/ may be expressed directly in terms i,j 1,0 0,1 of A , B , B , C and plz 1,z21 as follows: [i~_ nl0 p/zl,z2 / + A i,j where A ly.

Bull. Acad. Polon. Sci. Set. Sci. Techn. vol. XXX, no. 53-58. : Minimum energy control. Control and Cybernetics, vol. 121-131. : Controllability of M-dimensional systems. : Function of 2-D matrices. : New results in 2-D systems theory, part I : 2-D polynomial matrices, factorization and coprimeness, part ~ : 2-D state-space models realization and the notions of controllability, observability and minimality. Proc. 6, 1977. : Two-dimensional state-space discrete models for hyperbolic partial differential equations.

The result is a remainder of the form r/zl,z2/ = W/Zl,Z2/ - m/zl,z2/ P/Zl,Z2/ + nI n2 - 2i=I qlilz21 pi_llZl,Z21 - ~J=l q2jlzl I P-1'Jlzl with deg r/zl,z2/