Abstract:A variable order of state space modeling method is proposed by combining the principle of superposition of
fractional calculus operator. And the fractional order system is extended to the state space area and the minimum-order
state-space conversion is achieved. An order of the output signal is extracted through increasing state variables based on
actual needs. For the variable order of state space realization of fractional order systems where each order is less than 1, the
stability theorem is given for the variable fractional order system. Finally, simulation results show the effectiveness of the
method.