FINITE-TIME STABILITY IN MEAN FOR NABLA UNCERTAIN FRACTIONAL ORDER LINEAR DIFFERENCE SYSTEMS

Abstract

In this paper, the finite-time stability in mean for the uncertain fractional order linear time-invariant discrete systems is investigated. First, the uncertain fractional order difference equations with the nabla operators are introduced. Then, some conditions of finite-time stability in mean for the systems driven by the nabla uncertain fractional order difference equations with the fractional order [Formula: see text] are obtained by the property of Riemann–Liouville-type nabla difference and the generalized Gronwall inequality. Furthermore, based on these conditions, the state feedback controllers are designed. Finally, some examples are presented to illustrate the effectiveness of the results.