Delay-Dependent Stability Analysis and Design of Input-delayed Systems by Smooth Sliding Mode Control: Lagrange Theorem Approach

Jafarov E.

WSEAS Transactions on Systems and Control, vol.17, pp.269-278, 2022 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 17
  • Publication Date: 2022
  • Doi Number: 10.37394/23203.2022.17.31
  • Journal Name: WSEAS Transactions on Systems and Control
  • Journal Indexes: Scopus, INSPEC
  • Page Numbers: pp.269-278
  • Keywords: Input-delayed systems, Lagrange mean value theorem, Lyapunov-Krasovskii functional method, robust stabilization, sliding mode control
  • Istanbul Technical University Affiliated: Yes


© 2022, World Scientific and Engineering Academy and Society. All rights reserved.A new smooth sliding mode control design methodology based on Lagrange mean value theorem is proposed for stabilization of single input delayed systems. The Lagrange mean value theorem as a basic theorem of calculus is used for the design of linear sliding mode time-delay controller for the first time. This controller satisfies the sliding condition using a Zhou and Fisher type continuous control law eliminating the chattering effect. The constructive delay-dependent asymptotically stable sliding conditions are obtained by using the augmented Lyapunov-Krasovskii functionals and formulated in terms of simple (4x4)-matrix inequality with scalar elements. Developed design approach can be extended to robust stabilization of sliding system with unknown but bounded input delay. The maximum upper bounds of delay size can be found by using simple optimization algorithms. Helicopter hover control is considered as a design example for illustrating the usefulness of smooth sliding mode approach. Unstable helicopter dynamics are successfully stabilized by using linear sliding mode time-delay controller. For example, settling time is about 20 sec. Therefore, simulation results confirmed the effectiveness of proposed design methodology. Apparently, the proposed method has a great potential in design of time-delayed controllers.