Asymptotical stabilization of fractional-order linear systems in triangular form

In this paper, both state and output feedback stabilization controllers are designed for triangular fractional-order linear time-invariant (FO-LTI) systems with fractional-order 0<α<20<α<2. By introducing appropriate transformations of coordinates, the problems of control design are converted into the problems of finding some parameters, which can be certainly obtained by solving relevant matrix inequalities. Contrary to many existing linear matrix inequalities (LMIs)-based approaches, all the matrix inequalities involved for the systems under study always have feasible solutions. A simulation example is given to demonstrate the effectiveness of the proposed controllers.