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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

2 votes
1 answer
113 views

estimation of a vector-function

Let $x(t)\in C^1(\mathbb{R}_+,\mathbb{R}^m)$ be a vector-function such that 1) $\|x(t)\|+\|\dot x(t)\|\to 0$ as $t\to\infty$ and 2) for some real $c_1>0$ and all $t>0$ one has $\|x(t)\|\le c_1\|\dot …