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Analysis of invariant set for actuator saturation uncertain systems with disturbance

The set invariance problem is discussed for actuator saturation uncertain systems with disturbance. Under the linear state feedback control, the new condition of invariance ellipsoid is given for the addressed systems. By using composite quadratic Lyapunov function method and combining the convex additivity of linear matrix, it is shown that the convex hull of some invariant ellipsoids is also an invariant set, and the convex optimization method is given to enlarge the invariant set of the considered systems. Finally, the effectiveness of invariant set condition and convex optimal method is demonstrated by a numerical example.