# Conditions of a Monotonic Process?

$f$ is the output of a discrete time process described by

$f(k)=\sum\limits_{i=1}^{k-1}w_{ki}f(i)$

where $f(1)\geq0$ is a known initial condition and $w_{ki}\geq0$ are weights of previous states on the future states. Is it possible to derive a condition on the weights $w_{ki}$ such that the output is non-decreasing, i.e. $f(1)\leq f(2)\leq\cdots\leq f(k)\leq f(k+1)$

I feel expressing all subsequent states $f(k)$ directly in terms of $f(1)$ might help, but somehow the expression becomes unmanageable.

• Well, a condition that is only sufficient is: $w_{ki} \ge 1$, but to obtain a necessary condition is not that easy. You could try looking at the increment of your system, i.e. $\delta f(k) = f(k) - f(k-1)$ and rewrite all in those terms. You'll just have to find a condition for $\delta f$ to be positive, which may be easier. – politopo Mar 7 '14 at 10:03