Abstract

In this paper, the finite-time stability (FTS) and the finite-time boundedness (FTB) for the fractional order linear time invariant (LTI) systems with 0<α<1 are studied. First, some conditions to guarantee the FTS and the FTB for a class of fractional order LTI systems are derived by combining a new property for Caputo fractional derivatives, the generalized Gronwall inequality and the Laplace transform. Moreover, based on these conditions, the method for the design of state feedback controllers is presented. Finally, illustrative examples are provided to show the effectiveness of the results.

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