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This paper derives a somewhat surprising but interesting enough result on thestabilizability of discrete-time parameterized uncertain systems. Contrary toan intuition, it shows that the growth rate of a discrete-time stabilizablesystem with linear parameterization is not necessarily to be small all thetime. More specifically, to achieve the stabilizability, the system function$f(x)=O(|x|^b)$ with $b<4$ is only required for a very tiny fraction of $x$ in$\mathbb{R}$, even if it grows exponentially fast for the other $x$. Theproportion of the mentioned set in $\mathbb{R}$, where the system fulfills thegrowth rate $ O(|x|^b)$ has also been computed, for both the stabilizable andunstabilizable cases. This proportion, as indicated herein, could bearbitrarily small, while the corresponding system is stabilizable.

Is It Possible to Stabilize Disrete-time Parameterized Uncertain Systems Growing Exponentially Fast?