Feedback stabilisation control design for fractional order non-linear systems in the lower triangular form

Using the Lyapunov function method, this study investigates both state and output feedback stabilisation control design problems for fractional order non-linear systems in the lower triangular form, and presents a number of new results. First, some new properties for Caputo fractional derivative are presented. Second, by introducing appropriate transformations of coordinates, the feedback stabiliser design problem is converted into the determination of finding some parameters, which can be obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, both state and output feedback stabilisers are explicitly designed to make the closed-loop system asymptotically stable. The study of an illustrative example shows that the obtained results are effective in designing feedback stabilisers for fractional order non-linear systems in the lower triangular form.