Design of decentralised sliding surfaces for a class of large-scale systems with mismatched perturbations

Abstract

A novel design methodology of a decentralised sliding surface is proposed in this article for a class of large-scale systems with mismatched perturbations and interconnections. The main idea of this method is that the sliding surface function is obtained through a specially designed state transformation matrix. This transformation matrix, which includes the sliding surface coefficient function, contains adaptive mechanisms with the capability of adapting some unknown constants embedded in the least upper bounds of mismatched perturbations as well as interconnections, so that the perturbations (mismatched and matched) can be effectively overcome and asymptotical stability is guaranteed for each subsystem in the sliding mode. In addition, each decentralised controller also contains adaptive mechanisms to assure that the sliding mode is generated in a finite time without requiring the knowledge of upper bounds of the perturbations and interconnections. A practical example is also demonstrated by simulation for showing the feasibility of the proposed methodology.

Keywords:

• sliding mode control
• decentralised large-scale systems
• mismatched uncertainties
• Lyapunov stability theorem

Acknowledgements

The authors would like to thank the Editor, Associate Editor and the anonymous reviewers for their many helpful comments and suggestions that have helped to improve the quality of this article. Special thanks to Mr Yi-Jia Chiou, for his help in computer simulation. The authors are also grateful to the National Science Council of ROC for financial support for this research (NSC 95-2221-E-110-097).