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maxplusdelay

Max-plus algebra delay

Calling Sequence

[z] = maxplusdelay(x,d,T,A)

Parameters

x
: vector of real departure, may contain some delays
d
: vector of initial timetable
T
: timetable period, usually bigger than eigenvalue of A
A
: square input matrix
z
: matrix of delays

Description

This function returns z, the matrix that contains propagation of delays until the delay is gone.

The model of the system is given by

x(k+1) = A⊗x(k)⊕d(k+1), x(0)=x,

where d(k) is the schedulling vector. The timetable d(k) is realistic if for all k≥0

A⊗d(k) ≤ d(k+1).

For detail see: J.G. Braker, "Algorithms and Applications Timed Discrete Event Systems”, Ph.D thesis, Department of Technical Mathematics an Informatics Delft University of Technology, (1993).

Examples

A = [2. 7. -%inf 7. 2.; 
     -%inf -%inf 9. 2. -%inf;
     8. 6. 1. 5. -%inf; 
     0. 8. 6. 2. 2.;
     3. 7. 7. -%inf -%inf]; 
[lam,vx] = maxplusmaxalgol(A) 
d = [0;0;0;0;0]; 
x = [7;7;7;7;7]; 
T = 10;
z = maxplusdelay(x,d,T,A)
// This means that after k=4 the delay will be gone.

Author

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

See Also


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