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

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 0 < nu < 1 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.

Automated summary

This paper investigates the finite-time stability in mean for uncertain fractional order linear time-invariant discrete systems, introduces uncertain fractional order difference equations with nabla operators, establishes conditions for the systems driven by such equations, designs state feedback controllers, and provides examples to illustrate the effectiveness of the results.