Monotonicity Constraint

We can constrain the positive-time part of the window to be monotonically decreasing.

$\displaystyle \Delta h_{i}=h\left(i+1\right)-h\left(i\right)\leq 0\qquad i=1,\ldots ,L-1$

In matrix form,

$\displaystyle \left[\begin{array}{ccccc} -1 & 1 & & & 0\\ & -1 & 1 & & \\ & & \ddots & \ddots & \\ 0 & & & -1 & 1\end{array}\right]h$

$\displaystyle \le$

$\displaystyle 0,$

or,

$\displaystyle \zbox{\mathbf{D}\,h \le 0.}$