Finite-Time Stability for Caputo Nabla Fractional-Order Switched Linear Systems

Abstract

In this paper, we address the finite-time stability problem of Caputo nabla fractional-order switched linear systems with α∈(0,1). Firstly, the monotonicity of the discrete Mittag-Leffler function is proposed. Secondly, under the per-designed switching rules, the form of the solution for Caputo nabla fractional-order switched linear systems is obtained by using the discrete unit step function. On the above basis, some sufficient conditions of finite-time stability for Caputo nabla fractional-order switched linear systems are proposed, according to the discrete Grönwall inequality and the monotonicity of the discrete Mittag-Leffler function. Finally, simulation verification is carried out via three numerical examples.

Keywords

• finite-time stability
• Caputo nabla fractional-order switched linear systems
• discrete unit step function
• discrete Mittag-Leffler function