The feedback control of fractional order unified chaotic system

This paper studies the stability of the fractional orderunified chaotic system. On the unstable equilibrium points, the``equivalent passivity' method is used to design the nonlinearcontroller. With the definition of fractional derivatives andintegrals, the Lyapunov function is constructed by which it isproved that the controlled fractional order system is stable. WithLaplace transform theory, the equivalent integer order stateequation from the fractional order nonlinear system is obtained, and thesystem output can be solved. The simulation results validate theeffectiveness of the theory.