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maxplusctv

Max-plus algebra cycle time vector

Calling Sequence

[v] = maxplusctv(A)

Parameters

A
: square input matrix
v
: cycle time vector of the matrix A

Description

The function only valid for a square matrix A with at least one finite entry per row, and returns a cycle time vector v. The vector v equals to 1/k *( Ak ⊗x(0) ) for k to infite. This vector v is independent of initial vector x(0).

For details see: Gunawardena, J., "Cycle times and fixed points of min-max functions"; In G. Cohen and J.-P. Quadrat, editors, 11th International Conference on Analysis and Optimization of Systems, pp.266-272, Springer LNCIS, 199 (1994).

Examples

A = maxpluszeros(10,10);
A([8 39 47 58 75 80 82 91]) = 0;
A(11) = 84;
A(22) = 59;
A([33 93]) = 39;
A(45) = 38;
A(66) = 53;
A(71) = 12;
A(84) = 5;
A(86) = 67;
A(89) = 20;
A  =

 -Inf    84.  -Inf   -Inf   -Inf   -Inf  -Inf     12.  -Inf     0.   
 -Inf  -Inf     59.  -Inf   -Inf   -Inf  -Inf   -Inf     0.   -Inf   
 -Inf  -Inf   -Inf     39.  -Inf   -Inf  -Inf   -Inf   -Inf     39.  
 -Inf  -Inf   -Inf   -Inf   -Inf   -Inf  -Inf   -Inf     5.   -Inf   
 -Inf  -Inf   -Inf   -Inf     38.  -Inf  -Inf     0.   -Inf   -Inf   
 -Inf  -Inf   -Inf   -Inf   -Inf   -Inf    53.  -Inf     67.  -Inf   
 -Inf  -Inf   -Inf   -Inf     0.   -Inf  -Inf   -Inf   -Inf   -Inf   
   0.  -Inf   -Inf   -Inf   -Inf     0.  -Inf   -Inf   -Inf   -Inf   
 -Inf  -Inf   -Inf     0.   -Inf   -Inf  -Inf   -Inf     20.  -Inf   
 -Inf  -Inf   -Inf   -Inf   -Inf   -Inf  -Inf     0.   -Inf   -Inf   

v=maxplusctv(A)
v  =

   38.  
   38.  
   38.  
   20.  
   38.  
   38.  
   38.  
   38.  
   20.  
   38.

Author

"Max-Plus Algebra Toolbox", ver. 1.01, April, 2009.

See Also


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