State-feedback control system using adaptive observer for continuous-time linear fractional calculus system

Fractional calculus is the operation expanding the order of differential and integral operation from integer to non-integer order. By using fractional calculus, many complicated dynamics like visco-erastic body´s behavior or amorphous semiconductor´s electric behavior can be described as the simple system containing fractional order derivative (fractional order system). To control fractional order system containing unknown parameters, it is needed to observe plant´s state with identifying plant´s parameters. In this study, we design the adaptive observer for the fractional order system containing unknown parameters and construct the state-feedback control system.