Enlarging the domain of attraction and maximising convergence rate for delta operator systems with actuator saturation

Abstract

In this paper, we present some new approaches to improve the feedback property of delta operator systems with actuator saturation. Both enlarging the domain of attraction and maximising the convergence rate are the desired feedback properties. The lifting technique is used to enlarge the domain of attraction for the delta operator systems subject to actuator saturation. The maximisation of convergence rate is realised by designing control gain inside a given ellipsoid. A necessary and sufficient condition is proposed for the contractive invariance of the given ellipsoid. Simulation results are provided to demonstrate the effectiveness of the developed techniques.

Keywords:

• Delta operator system
• actuator saturation
• domain of attraction
• lifting technique
• convergence rate

Acknowledgements

The authors would like to thank the anonymous reviewers for their detailed comments which helped to improve the quality of the paper. The work of Hongjiu Yang was supported by the National Natural Science Foundation of China (61203023), the Natural Science Foundation of Hebei Education Department (Q2012060), and the Hebei Provincial Natural Science Fund (E2014203122, F2013203092). This work was partially supported by the Australian Research Council (DP140102180, LP140100471, LE150100079), and the 111 Project (B12018).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work of Hongjiu Yang was supported by the National Natural Science Foundation of China [grant number 61203023]; the Natural Science Foundation of Hebei Education Department [grant number Q2012060]; the Hebei Provincial Natural Science Fund [garnt number E2014203122], [grant number F2013203092]. This work was partially supported by the Australian Research Council [grant number DP140102180], [garnt number LP140100471], [grant number LE150100079]; the 111 Project [garnt number B12018].