LMI Conditions for Robust Invariance of the Convex Hull of Ellipsoids with Application to Nonlinear State Feedback Control

The convex hull of ellipsoids was suggested in the literature for robust invariance of constrained uncertain and/or time-varying linear discrete-time systems. It was show that a robust invariant set obtained with the convex hull of ellipsoids can be significantly larger than that with the ellipsoidal set. However, the design conditions are given in terms of bilinear matrix inequalities (BMIs), which are non-convex. The main purpose of this paper is to present a way to overcome this weakness by providing new convex linear matrix inequality (LMI) design conditions. It is shown that the conditions are losslessly extended to robust controlled invariance and to nonlinear state feedback control design. Two examples are included with comparison to earlier solutions from the literature to illustrate the results.