Stability analysis of interconnected nonlinear fractional-order systems via a single-state variable control

This paper is devoted to investigating the stability of interconnected nonlinear fractional-order systems via a single-state variable control. First of all, based on stability theory, the Gronwall-Bellman lemma and the Mittag-Leffler function, the relevant stability results are derived. The obtained results are general and can further extend the application range. Meanwhile, an improved single-state variable control method is introduced. The control scheme only needs to control some state variable of the system or some subsystem(s) to realize and any additional restrictions are not added. Finally, the effectiveness of the obtained results is demonstrated by several typical examples. Besides, by comparison, simulation results show that the proposed control method can indeed decrease the design and control cost and improve flexibility of control.