Fixed-time integral sliding mode control design for a class of uncertain nonlinear systems based on a novel fixed-time stability condition

This paper develops a different approach to fixed-time controller design by introducing a totally novel fixed-time stability condition formulated according to the Lyapunov function technique. Based on this condition, a fixed-time sliding mode control law is derived for a class of uncertain nonlinear systems. This controller assures complete robustness of the closed-loop system against matched uncertainties and exogenous disturbances from the beginning owing to the elimination of the reaching phase by benefiting from a novel integral terminal sliding surface. This surface constructed in accordance with the proposed condition determines whole dynamics of the closed-loop system and guarantees its fixed-time stability. Numerical simulations are reported to validate the effectiveness of the theoretical results. (c) 2022 European Control Association. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a novel approach to fixed-time controller design by introducing a new fixed-time stability condition based on the Lyapunov function technique. A fixed-time sliding mode control law is derived for uncertain nonlinear systems using this condition. The controller ensures robustness of the closed-loop system against matched uncertainties and exogenous disturbances from the beginning by eliminating the reaching phase through an integral terminal sliding surface. This surface determines the dynamics of the closed-loop system and guarantees its fixed-time stability. Numerical simulations validate the effectiveness of the proposed theoretical results.