The The ultimate bound and positively invariant set for the general n-D continuous-time autonomous system

Abstract

In the present paper, we investigate the ultimate bound and positively  invariant set for the general n-D continuous-time system using a technique combining the generalized Lyapunov function theory and optimisation.
Especially, we report suffcient conditions for this system to be contained in a n-dimensional ellipsoidal set. Furthermore, by using the multivariable functions analysis, we generalize all the existing results in the relevant literature concerning the finding of the upper bound for the given system.