The feedback control of fractional order unified chaotic system

Abstract

This paper studies the stability of the fractional order unified chaotic system. On the unstable equilibrium points, the “equivalent passivity" method is used to design the nonlinear controller. With the definition of fractional derivatives and integrals, the Lyapunov function is constructed by which it is proved that the controlled fractional order system is stable. With Laplace transform theory, the equivalent integer order state equation from the fractional order nonlinear system is obtained, and the system output can be solved. The simulation results validate the effectiveness of the theory.