Robust H_∞ control for a class of uncertain mechanical systems

Abstract

In this article, the problem of H _∞ control is investigated for a class of mechanical systems with input delay and parameter uncertainties which appear in all the mass, damping and stiffness matrices. Two approaches, norm-bounded and linear fractional transformation (LFT) uncertainty formulations, are considered. By using a new Lyapunov–Krasovskii functional approach, combined with the advanced techniques for achieving delay dependence, improved robust H _∞ state-feedback controller design methods are developed. The existence condition for admissible controllers is formulated in the form of linear matrix inequalities (LMIs), and the controller design is cast into a convex optimisation problem subject to LMI constraints. If the optimisation problem is solvable, a desired controller can be readily constructed. The result for the norm-bounded uncertainty case improves the existing ones in terms of design conservatism, and that for the LFT uncertainty case represents the first attempt in this direction. An illustrative example is provided to show the effectiveness and advantage of the proposed controller design methodologies.

Keywords:

• H _∞ control
• input delay
• linear matrix inequalities
• mechanical systems
• parameter uncertainties

Acknowledgements

This work was partially supported by National Natural Science Foundation of China (60825303), Foundation for Distinguished Young Scholars of Heilongjiang Province of China (JC200809), Foundation for the Author of National Excellent Doctoral Dissertation of China (2007E4), 973 Project (2009CB320600) and the Engineering and Physical Sciences Research Council, UK (EP/F029195).