'grows to infinity' is correct and usable in written English.
You can use this phrase to indicate something increasing, expanding, or growing without limit or end. For example, "As the population expands, traffic congestion in the city grows to infinity."
Nothing grows to infinity.
To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits.
As this ratio grows to infinity, the phase portrait changes and the process approaches a batch behaviour so that the stability analysis for that case may be applied.
First, when all the states are subjected to constraints, we employ a Barrier Lyapunov Function (BLF), which grows to infinity whenever its arguments approach some finite limits, to prevent the states from violating the constraints.
When the graph is complete and the numbers of particles grows to infinity, the system is well-described by a McKean-Vlasov equation, which describes the behavior of one typical particle.
The uniformly bounded stability of the closed-loop system is achieved through rigorous Lyapunov analysis without any discretisation or simplification of the dynamics in the time and space, and the state observer error is ensured to exponentially converge to zero as time grows to infinity.
Our first goal is to prevent the queue lengths Q n (t) from growing to infinity.
"However, mountains don't grow to infinity, so there must be another mechanism which has lowered the summit of Europe.
If the initial status Q → ( 0 ) is not infinity, then the queue lengths will not grow to infinity, which proves the stability of BA-MW-PCC.
To make derivations possible, the asymptotic regime, where all the system dimensions grow to infinity with a constant pace, has been considered.
