A Lipschitz continuous sliding mode control for implicit systems

摘要

In this paper, implicit systems with uncertain input matrix subjected to matched Lipschitz disturbances are considered. For such kind of systems a Lipschitz continuous control, achieving admissible solutions for implicit systems is proposed. The developed methodology consists of two steps. In the first step a stable sliding surface is designed after transforming the original system into a regular like form. Then a first order sliding mode controller through an integrator is designed which will ensure finite-time convergence to the sliding manifold and the exponential convergence to the origin in spite of the presence of Lipschitz disturbances and uncertain input matrix.(c) 2022 European Control Association. Published by Elsevier Ltd. All rights reserved.