Stabilization of a 4D financial system with disturbance and uncertainty by UDE-based control method

Abstract

The stabilization of the 4D financial system involving the external disturbance and uncertainty is investigated extensively. Firstly, two types of controllers (us) are proposed to stabilize the nominal 4D financial system which is not impacted by the external disturbances. Secondly, three kinds of filters are designed, based on which, three categories of uncertainty and disturbance estimators (uude) are presented and used to asymptotically counteract the lumped disturbance and uncertainty (ud), i.e., buude=−uˆd→−ud, as t→∞, where uˆd is the estimate of ud and b is a known vector. Consequently, the stabilization problem of such a system is implemented by the combined controllers (u=us+uude). It is noted that the obtained controllers are single input controllers, and thus easy to be implemented in applications. Finally, the proposed theoretical results are demonstrated and verified by the computer simulation.