On the ellipsoidal invariant set of fractional order systems subject to actuator saturation

This paper investigates the method for estimating the domain of attraction of the origin for a class of fractional order system subject to actuator saturation with the fractional order 0 < α < 1. The sufficient condition on the asymptotic stability are obtained using Lyapunov direct approach and fractional order inequality. The method for the estimation on the contractively invariant ellipsoid is derived in terms of linear matrix inequalities (LMIs), and hence can be easily adopted for controller synthesis. Two numerical examples are provided to illustrate the effectiveness of the developed method.