A question on contral parameters in dynamical systems?

Hi gurus,
I have an urgent question on contral parameters in dynamical systems. I would greatly appreciate your help!
Suppose we have a dynamic system as
\dot = f (x, \beta), where x is nx1 vector and \beta is a vector of continuous-time control variables (with the same dimension as x).
Consider the following optimization problem:
min g(x, \beta) subject to \dot = f (x, \beta) 0 <= \beta <= UB
Since the objetive function is continuous, and the constraint set is convex and compact, the solution of \beta must exist.
My questions is: if we add one more constraint, A<= \dot <B, then whether can we say the constraint set is still convex and compact????
Thank you very much,
Fan
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In article <35e4cfd5-01bd-4cde-8006-

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