Finite-time stability in measure for nabla uncertain discrete linear fractional order systems

Abstract

With the development of mathematical theory, fractional order equation is becoming a potential tool in the context of neural networks. This paper primarily concerns with the stability for systems governed by the linear fractional order uncertain difference equations, which may properly portray neural networks. First, the solutions of these linear difference equations are provided. Secondly, the definition of finite-time stability in measure for the proposed systems is introduced. Furthermore, some sufficient conditions checking for it are achieved by the property of fractional order difference and uncertainty theory. Besides, the relationship between finite-time stability almost surely and in measure is discussed. Finally, some numerical examples are analysed by employing the proposed results.