Positively invariant sets play an important role in the theory and
applications of dynamical systems. The stability in the sense of
Lyapunov of the equilibrium x = 0 is equivalent to the existence of the
ellipsoidal positively invariant sets. The constraints on the state and
control vectors of dynamical systems can be formulated as polyhedral
positively invariant sets in practical engineering problems. Numerical
checking method of positive invariance of polyhedral sets is addressed
in this paper. The validation of the positively invariant sets can be
done by solving LPs which can be easily done numerically. It is
illustrated by examples that our checking method is effective. Compared
with the now existing algebraic methods, numerical checking method is an
attractive method in that it’s easy to be implemented.
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