Stability analysis of switched fractional-order continuous-time systems.

In this paper, a class of switched fractional-order continuous-time systems with order 0 < α < 1 is investigated. First, an interesting property of fractional calculus is revealed, that is, unlike integer-order integral, it does not hold that t 0 D t - α f (t) = t 0 D t 1 - α f (t) + t 1 D t - α f (t) for α > 0 , t 0 < t 1 < t , not to mention fractional derivative. Then, a general formula of solutions for a piecewise-defined differential function with Caputo fractional derivative is introduced. After that, based on the derived equivalent solution of fractional-order piecewise-defined functions, the problem of finite-time stability for a class of switched fractional-order systems is reconsidered. Finally, two illustrative examples are provided to demonstrate the effectiveness of the presented sufficient conditions, respectively. [ABSTRACT FROM AUTHOR]