Brief paper: Sliding-mode observers for systems with unknown inputs: A high-gain approach

Authors:
Karanjit Kalsi;Jianming Lian;Stefen Hui;Stanislaw H. Żak
Affiliations:
School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA;Department of Mathematical Sciences, San Diego State University, San Diego, CA 92182, USA;School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907, USA
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

Sliding-mode observers can be constructed for systems with unknown inputs if the so-called observer matching condition is satisfied. However, most systems do not satisfy this condition. To construct sliding-mode observers for systems that do not satisfy the observer matching condition, auxiliary outputs are generated using high-gain approximate differentiators and then employed in the design of sliding-mode observers. The state estimation error of the proposed high-gain approximate differentiator based sliding-mode observer is shown to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. Finally, the unknown input reconstruction using the proposed observer is analyzed and then illustrated with a numerical example.