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Min-Max-Plus And Petrinet >> Min-Max-Plus And Petrinet > minmaxpluspowalgol

minmaxpluspowalgol

Bipartite Min-Max-plus algebra eigenvalue and eigenvector

Calling Sequence

[eigval,eigvec] = minmaxpluspowalgol(A,B)

Parameters

A
: input matrix have of size n x m .
B
: input matrix have of size m x n .
eigenval
: an eigenvalue of the matrix ℳ=(A,B)
eigvec
: a corresponding eigenvector of the matrix ℳ=(A,B) of size ( (n∔m) x 1 .

Description

Bipartite min-max-plus system given by equations

x(+1) = A⊗y(k) and y(k) = B⊗' x(k) for k = 0,1,2,⋯ (1)

where A∊ℝεn×m, B ∊ℝT m×n, x(k)∊ℝεn, and y(k) ∊ℝT m

The equation (1) can be written as a simple notation that is given by :

z(k+1) = ℳ(z(k)) ....(2)

where z(k)=(x(k),y(k))t, ℳ((x(k),y(k))t )=(A⊗y(k),B⊗'x(k))t .

The function returns eigenvector and an unique corresponding eigenvalue of matrix ℳ=(A,B) of size n∔m . According to the reference below, assumption of the function, the periodic behaviour of bipartite of min-max-plus system (1) is constant.

For details see: Subiono and J.van der Woude (2000); "Power algorithms for (max,∔)- and bipartite (min,max,∔)-systems"; DEDS, vol.10, pp.369-389, 2000.

Examples

A =[2  -3 6 2 -11;
       13 12 19 -6 21;
       -10 8 14 -5 -16];
B =[16 8 4;
       -11 10 14;
       -8 -4 4;
       13 -1 -7;
       4 7 0];

[eigval,eigvec] = minmaxpluspowalgol(A,B)

Author

"Min-Max-Plus Algebra And Petrinet Toolbox", ver. 2.1.0, January, 2017.

See Also


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