Finite-time attractivity analysis for nonautonomous dynamical systems with uncertainty

Uncertain dynamical system driven by Liu process is of importance to depict the operation laws of real systems disturbed by human epistemic uncertainty. This paper mainly investigates the finite-time attractivity of uncertain dynamical systems. New concepts of the finite-time attractivity are first introduced for uncertain dynamical systems from different perspectives, and the relationships among these types of concepts are revealed based on uncertainty theory. The judgement theorems for ensuring the finite-time exponential attractivity of two classes of uncertain dynamical systems are proposed, respectively. Several examples are provided to illustrate the main concepts and results derived. Finally, the uncertain mean-reverting process with time-varying parameters is considered as an application.