A descriptor system approach to robust H_∞ control for linear systems with time-varying uncertainties

Abstract

This article addresses the problems of robust H _∞ performance analysis and synthesis for continuous-time linear systems with time-varying uncertainties using parameter-dependent Lyapunov functions. An H _∞ performance criterion in terms of linear matrix inequalities is derived via employing a descriptor model transformation of linear systems with polytopic uncertainties (polytopic systems). This H _∞ performance criterion can be applied to robust controller synthesis and filtering design. The descriptor system approach is also taken to explore robust H _∞ performance analysis and controller synthesis of affine parameter systems. A flight control system and two numerical examples are given to illustrate the effectiveness of the proposed analysis and synthesis procedures.

Keywords:

• H _∞ control
• descriptor system approach
• affine parameter systems
• polytopic systems
• parameter-dependent Lyapunov functions

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous reviewers for their helpful and insightful comments for further improving the quality and presentation of this article. This work was supported by the National Natural Science Foundation of China under grants 60874024 and 90816028, the Specialized Research Fund for the Doctoral Program of Higher Education of China under grant 200801450019, and in part by the Ministry of Education and Science of Macedonia under grant 14-3154/1-17.12.2007.