Brief paper: Further results on the disturbance response of a double integrator controlled by a saturating linear static state feedback

Authors:
Xu Wang;Ali Saberi;Anton A. Stoorvogel;Håvard Fjær Grip
Affiliations:
School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA;Department of Electrical Engineering, Mathematics, and Computing Science, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA
Venue:
Automatica (Journal of IFAC)
Year:
2012

Citing 2
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On characterizations of the input-to-state stability property

Systems & Control Letters
Technical communique: On the disturbance response and external stability of a saturating static-feedback-controlled double integrator

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Simultaneous external and internal stabilization of linear systems with input saturation and non-input-additive sustained disturbances

Automatica (Journal of IFAC)

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Abstract

In this paper, we study the response to external disturbances of a double integrator with a saturating feedback. For a class of disturbances that have bounded integrals over all intervals, we show that a linear static feedback law can always be designed to ensure boundedness of the states. Moreover, boundedness can be preserved if the disturbance is biased by a small DC signal. In the special case that the disturbance is made up of a finite number of sinusoids and a small bias, any linear static feedback ensures boundedness of the states. These results are an extension of previous results by Wen, Roy, and Saberi (2008).