- 302
- 73
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 all ##t>0## one has ##\|x(t)\|\le c_1\|\dot x(t)\|##
Is it true that ##\|x(t)\|\le c_2 e^{-c_3t}##? Here ##c_i## are positive constants.
1) ##\|x(t)\|+\|\dot x(t)\|\to 0## as ##t\to\infty## and
2) for all ##t>0## one has ##\|x(t)\|\le c_1\|\dot x(t)\|##
Is it true that ##\|x(t)\|\le c_2 e^{-c_3t}##? Here ##c_i## are positive constants.