Comment on 'Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization' [Chaos, Solitons and Fractals 44 (2011) 137-144]

摘要

In the commented paper the authors investigate the ultimate bound and positively invariant set of a permanent magnet synchronous motor system. The three-dimensional system they deal with is given by x = -x + yz, ? = -y + γz - xz, ? = σ(y - z), where c and r are positive parameters. However, by interchanging the variables x and z, this system is exactly the classical Lorenz system X = σ(Y - X), Y = ρX - Y - XZ, ? = -bZ + XY, for β = 1 and ρ = γ. Therefore, it is not necessary to reobtain these results for the permanent magnet synchronous motor system as the authors do because the results found in the literature on the ultimate bound and positively invariant set for the Lorenz system can be applied.