On invariant ellipsoid for linear systems by saturated controls

Recently a necessary and sufficient condition for that an ellipsoid can be made contractively invariant by bounded controls was reported in the literature, which is characterized in terms of an algebraic Riccati inequality. In this paper we show that the condition concerning algebraic Riccati inequality may be very restrictive in some case, and can be relaxed to algebraic Riccati equation having positive definite solution. Therefore it allows to obtain less conservative estimation of the maximal invariant region. In particular, analytical characterization of a class of maximal invariant ellipsoid is obtained by using this less conservative technique. In some case, the relationship between the results and the absolute stability theory is revealed. Example shows the efficiency of the proposed approach.