State feedback with fractional PIλ Dλ control structure for fractional Lü chaos stabilization

摘要

This paper focuses on the study of the behavior of the fractional Lü system and chaos suppression using a fractional order proportional integral derivative controller PIλDλ. Stability analysis of the nonlinear chaotic system is performed using the bifurcation diagram. Then the fractional order λ is selected by means of a quadratic criterion. We show by numerical simulations that the fractional PIλDλ controller provides the best closed loop system performance for stabilizing the problem of unstable fixed point.