Stabilization of linear systems by state feedback is an important problem of the controller design. The design of observers with appropriate error dynamics is a dual problem. This duality leads, at first glance, to the equivalence of the responses in the synthesized systems. This is true for the time-invariant case, but may not hold for time-varying systems. We limit ourselves in this work by the situation when the system itself is time invariant, and only the gains are time varying. The possibility of assigning a rapidly decaying response without peaking is analyzed. The solution of this problem for observers using time-varying gains is presented. Then we show that this result cannot be obtained for state feedback controllers. We also analyze the conditions under which the observer error dynamics and the response of the closed loop time-varying controllers are equivalent. Finally we compare our results to recently proposed observer converging in finite time and Riccati-based continuous observer with limited overshoots.
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June 2005
Technical Papers
Observer and Controller Design Using Time-Varying Gains: Duality and Distinctions
Vladimir Polotski
e-mail: vpolotski@frontline-robotics.ca
Vladimir Polotski
Frontline Robotics
, 1920 Research Road, U62, NRC Uplands Campus Ottawa, ON K1V984, Canada Fax: (613) 739–2687
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Vladimir Polotski
Frontline Robotics
, 1920 Research Road, U62, NRC Uplands Campus Ottawa, ON K1V984, Canada Fax: (613) 739–2687e-mail: vpolotski@frontline-robotics.ca
J. Dyn. Sys., Meas., Control. Jun 2005, 127(2): 267-274 (8 pages)
Published Online: July 14, 2004
Article history
Received:
July 5, 2002
Revised:
July 14, 2004
Citation
Polotski, V. (July 14, 2004). "Observer and Controller Design Using Time-Varying Gains: Duality and Distinctions." ASME. J. Dyn. Sys., Meas., Control. June 2005; 127(2): 267–274. https://doi.org/10.1115/1.1898230
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