Piecewise-continuous observers for linear systems with sampled and delayed output

Abstract

The paper presents a new class of state observers for linear systems with sampled and delayed output measurements. These observers are derived using the theory of a particular class of hybrid systems called piecewise-continuous systems, and can be easily implemented. The performances of the piecewise-continuous observers are compared with the performances of state observers designed using the Lyapunov–Krasovskii techniques. A piecewise-continuous observer is designed and implemented to an experimental visual servoing platform.

Keywords:

• piecewise-continuous systems
• sampled and delayed output measurements
• piecewise-continuous observer
• visual servoing systems

Acknowledgements

The authors would like to thank the reviewers and editors for their help and comments to improve the quality of the paper.

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 61304077], [grant number 61203115]; Natural Science Foundation of Jiangsu Province [grant number BK20130765]; Specialized Research Fund for the Doctoral Program of Higher Education of China [grant number 20123219120038]; Chinese Ministry of Education Project of Humanities and Social Sciences [grant number 13YJCZH171]; Fundamental Research Funds for the Central Universities [grant number 30920130111014]; Zijin Intelligent Program of Nanjing University of Science and Technology [grant number 2013_ZJ_0105].

Notes on contributors

H.P. Wang

Haoping Wang received the PhD degree in automatic control from Lille University of Science and Technology (LUST), France, in 2008. He is currently an associate professor and PhD supervisor at Automation School and director of Sino-French International Joint Laboratory of Automatic Control and Signal Processing, Nanjing University of Science and Technology, China. He was research fellow at MIS Laboratory of Picardie University and at LAGIS of LUST, France. His research interests include the theory and applications of hybrid systems, visual servo control, friction modelling and compensation, modelling and control of diesel engines, biotechnological processes and wind turbine systems.

Y. Tian

Yang Tian received the PhD degree in automatic control from Ecole Centrale de Lille, France, in 2010. She is currently a lecturer at Automation School, Nanjing University of Science and Technology, China. She was assistant professor of LAGIS at Lille University of Science and Technology. Her research interests include nonlinear and hybrid systems theory and applications, and algebraic-differential methods in control and estimation theory.

N. Christov

Nicolai Christov is a professor of LAGIS at Lille University of Science and Technology. His research interests are in linear systems theory, optimal and robust control and estimation, and sensitivity analysis and numerical methods for linear systems.