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maxplusposegv

Max-plus algebra possible eigenvector of interval matrices

Calling Sequence

[As,lx] = maxplusposegv(A,B,x)

Parameters

A
: an input square matrix of size n by-n in
B
: an input square matrix of size n by-n
x
: an input vector dimension n
As
: an output square matrix of size n by-n such that A≤As≤B.
lx
: an outnput scalar that is an eigenvalue of matrix As.

Description

Function returns an possible eigenvalue lx and matrix As that satisfies

A≤As≤B, As⊗x = lx⊗x, and A⊗x ≤ As⊗x ≤ B⊗x.

And returns As=[], ls=[] if the vector x is not possible eigenvector of interval matrices. For more detailed, see: Cechlarova, K. (2005), "Eigenvectors of Interval Matrices over Max-Plus Algebra", Discrete Applied Mathematics, vol.150, 2-15.

Examples

A  = [2. 6. 6. 2. 3.;  
      8. 8. 7. 2. 9.;  
      0. 7. 7. 2. 2.;  
      3. 9. 2. 9. 3.;  
      7. 1. 5. 7. 4.];
B  = [3. 15. 9. 3. 7.;   
      16. 14. 10. 11. 12.;  
      5. 13. 15. 8. 7. ;  
      3. 16. 3. 12. 8.;   
      16. 4. 14. 11. 4.];
x = [6;7;9;5;3]; 
[As,lx]=maxplusposegv(A,B,x)
// Check that A⊗x≤As⊗≤B⊗x
maxplusotimes(A,x)<=maxplusotimes(As,x)&maxplusotimes(As,x)<=maxplusotimes(B,x)

Author

"Max-Plus Algebra And Petrinet Toolbox", ver. 1.1.0, February, 2013.

See Also


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