A non-linear/uncertain system is quadratically bounded if all its solutions are bounded and this is guaranteed by a quadratic Lyapunov function. We obtain easily checkable conditions which are necessary and sufficient for a class of nominally linear systems to be quadratically bounded. The results are applied to the rotational motion of an axisymmetric spacecraft subject to unknown but bounded disturbance torques.
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Brockman et al. (1998) studied this question.