Abstract: In order to solve the problem of passive synchronization control of fractional order Lorenz systems with
different dimensions，according to the stability theory and passive control theory of fractional-order system，a new
active controller and passive controller are designed to make the system realize the effect of synchronous tracking，
and to achieve passive synchronization of fractional-order systems with different dimensions under different initial
conditions． This method extends the passive synchronization control of integer order chaotic systems for the same
dimension and structure to the different dimension fractional order system with order less than 1． The numerical
simulation results verify the feasibility and effectiveness of the designed controller． The driving system can keep
the same trajectory with the state variables of the response system，and the control method is specific and fast．

Key words: different dimensional fractional-order, passive control, chaotic system, hyperchaotic system