H_∞ output tracking control for delta operator systems with insensitivity to controller coefficient variations

Abstract

The problem of designing insensitive H _∞ output tracking controller for discrete-time systems is studied in a unified framework by using the delta operator approach. A type of coefficient sensitivity performance measure is first developed tomeasure the sensitivity of the transfer function with respect to controller coefficient variations, and the corresponding controller design problem is naturally reformulated as a mixed-objective H _∞ control problem. It is worth mentioning that a novel bounded real lemma (BRL), i.e. Theorem 1 in this article, for delta operator systems is obtained, which is adapted to deal with the multi-objective optimisation problem or polytopic uncertain systems in a potentially less conservative framework. Then, based on the novel lemma, an linear matrix inequality (LMI)-based design method is proposed for achieving the output tracking purpose. Finally, a numerical example based on the linearised model of F-18 aircraft is given to illustrate the effectiveness of the proposed method.

Keywords:

• delta operator systems
• output tracking controller
• controller coefficient variations
• linear matrix inequality

Acknowledgements

This work was supported in part by the Funds for Creative Research Groups of China (No. 60821063), National 973 Program of China (Grant No. 2009CB320604), the Funds of National Science of China (Grant No. 60974043, Grant No. 60904010, Grant No. 60804024), and the 111 Project (B08015), the Funds of Doctoral Program of Ministry of Education, China (20100042110027), the Fundamental Research Funds for the Central Universities (No. N090604001), China Postdoctoral Science Foundation (No. 2009045127, No. 201003624).