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IMA Journal of Mathematical Control and Information 2004 21(4):393-418; doi:10.1093/imamci/21.4.393
© 2004 by Institute of Mathematics and its Applications
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Using delays and time-varying gains to improve the static output feedback stabilizability of linear systems: a comparison

Wim Michiels1,*, Silviu-Iulian Niculescu2 and Luc Moreau3

1 K.U. Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Heverlee, Belgium, 2 Heudiasyc, UTC, UMR CNRS 6599, BP 20529, 60205 Compiègne, France, 3 Ghent University, EESA-SYSTeMS, Technologiepark 914, 9052 Zwijnaarde, Belgium

We address the output feedback stabilization problem of linear finite-dimensional SISO systems. Limitations of static time-invariant output feedback on stabilizability are well known. We investigate and compare the possibilities of two recently proposed simple modifications/generalizations of static time-invariant output feedback to remove such limitations. The first approach consists of introducing a time-delay in the control law, which can be treated as an additional control parameter. The second approach consists of making the gain time-varying. We show that both approaches are complementary. Existing theoretical results are brought together in a unifying framework. Numerical procedures for the construction of the controllers are provided. Robustness w.r.t. both parametric and delay uncertainty are dealt with. As an illustration the stabilizability of all second-order systems is completely determined.

Keywords: output feedback; stabilization; delay equations; non-autonomous systems.

Received 1 August 2003.

* Corresponding author. Email: Wim.Michiels{at}cs.kuleuven.ac.be


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