Finite-time stability and finite-time boundedness of uncertain fractional order switched systems

In recent years, fractional order systems have received much attention due to the excellent ability to model the dynamics of complex systems. Stability is an important index to measure the performance of the system. The finite-time stability can reflect the transient performance of the system, which is significant in practical applications. Therefore, the issue of the finite-time stability (FTS) and the finite-time boundedness (FTB) for the uncertain fractional order switched systems is investigated. The state feedback controller is designed to achieve the desired system performance. By utilizing the Lyapunov functions method and average dwell time approach, some sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to guarantee the FTS and the FTB of the closed-loop systems. In addition, a method is given to obtain the state feedback controller gains. Finally, two numerical examples are provided to show the effectiveness of the main results.