Control of a perturbed chaotic system by using a trajectory trapping strategy

This paper proposed a trajectory sliding control strategy for a nonlinear chaotic system subject to external disturbance. For a given chaotic system, a trapping region is designed based on the invariant ellipsoid control method. Existence of the control region is characterized by a feasibility issue of linear matrix inequalities. According to the path information of the chaotic system, we classify the trajectories by a couple of ellipsoid regions subject to volume minimization. Then a target trapping region that the center locates close to the designed sliding surface is determined. As a result, when the trajectories of the chaotic system enter the prescribed region, it will be trapped inside the invariant ellipsoid for all the subsequent time and finally be guided toward to the origin. Numerical simulations are given to demonstrate the effectiveness and the advantages of the proposed trajectory trapping control approach.