On the tightness of a recent set invariance condition under actuator saturation

A su/cient condition for an ellipsoid to be invariant was obtained recently and an LMI approach was developed to 3nd the largest ellipsoid satisfying the condition. This condition was later shown to be necessary for the single input case. This paper is dedicated to the multi-input case. We will examine the conservatism of the condition for multi-input systems. Our investigation is conducted by studying the optimal solution to a related LMI problem. A criterion is presented to determine when the condition is not conservative and when the largest invariant ellipsoid has been obtained by using the LMI method. c © 2003 Elsevier B.V. All rights reserved.