Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization

► We combine the Lyapunov stability theory with the comparison principle method to study the ultimate bound and positively invariant set for a synchronous motor system. ► A three-dimensional ellipsoidal ultimate bound and positively invariant set is obtained for all the positive values of its parameters σ, γ. ► The two-dimensional estimation with respect to x − y and x − z are also established. ► The result is applied to the study of completely chaos synchronization. ► Numerical simulations are presented to show the effectiveness of the proposed scheme.