Abstract
Ellipsoidal invariant sets of linear discrete-time systems are treated to approximate the reachable sets for bounded inputs. All the ellipsoids are parameterized by a bilinear matrix inequality. The criteria for the ellipsoids are defined to represent the degrees of approximations. The optimal ellipsoids can be obtained by the convex optimizations with one scalar variable. The efficiency of the proposed method is demonstrated in a numerical example in comparison with a method of previous research.
