Max-plus algebra delay
[z] = maxplusdelay(x,d,T,A)
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).
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. | ![]() | ![]() |