Stability and robust stabilization of uncertain switched fractional order systems.

In this paper, the stability and robust stabilization of switched fractional order systems are concerned. Firstly, two stability theorems for switched fractional order systems with order 0<α<1 and 1<α<2 under the arbitrary switching law are given. Secondly, the relationship between the stability of switched integer order systems and that of switched fractional order systems is obtained. Finally, the robust stabilization of uncertain switched fractional order systems under the common switching law is further discussed. The state feedback control gains are obtained under both the sensor and actuator faults in terms of linear matrix inequalities. A practical electrical circuit example and four numerical simulation examples are presented to show the effectiveness of our results.