Delay-fractioning-dependent robust H_∞ control for linear systems with delay in state or input and its applications

Abstract

A new delay fraction technique is proposed to investigate the H _∞ control of uncertain systems with time delay in state or input. First, the variation interval of the time-varying delay is divided into several subintervals with equal length. By checking the variation of derivative of the Lyapunov functional in every subinterval, some new criteria on H _∞ performance analysis of the systems are derived in terms of the convexity properties of a matrix inequality and some other new analysis techniques. Then, criteria for the H _∞ control design are presented, which are concluded from the H _∞ performance analysis results. As applications of the derived results, H _∞ performance analysis and H _∞ control design are carried out for some systems, including two numerical systems, linearised truck trailer system and traffic network system. Discussions show that, the proposed method is effective for these systems and much less conservativeness appears than those given in the existing references.

Keywords:

• delay-fraction-dependent
• interval time-varying delay
• Lyapunov–Krasovskii functional

Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant (60834002, 60904013, 51075215 and 61074024) and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant (09KJB510004).