Variable structure control of linear time invariant fractional order systems using a finite number of state feedback law

In this paper, an approach based on the variable structure control is proposed for stabilization of linear time invariant fractional order systems (LTI-FOS) using a finite number of available state feedback controls, none of which is capable of stabilizing the LTI-FOS by itself. First, a system with integer order derivatives is defined and its existence is proved, which has stability equivalent properties with respect to the fractional system. This makes it possible to use Lyapunov function and convex analysis in order to define the sliding sector and develop a variable structure control which enables the switching between available control gains and stabilizing the fractional order system.