# $H_\infty$ control with state feedback

A.A. Stoorvogel

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1 Citation (Scopus)

## Abstract

This paper considers H∞-control under the assumption that all the states are available for feedback. It can be shown that in that case we can restrain ourselves to static feedback. This paper gives extensions and a more intuitive explanation of recent results. Under a number of assumptions necessary and sufficient conditions are given for the existence of a stabilizing feedback such that the closed loop system has H∞ norm less than or equal to some predetermined bound γ. It is shown that if these assumptions are not met then by disturbing the system in such a way that these assumptions are satisfied we can find results about the existence of these desired feedbacks in more general cases.
Original language English Robust Control of Linear Systems and Nonlinear Control (Proceedings of the International Symposium on Mathematical Theory of Networks and Systems, MTNS-89, Amsterdam, The Netherlands, June 19-23, 1989) M.A. Kaashoek Basel Birkhäuser Verlag 347-354 2 https://doi.org/10.1007/978-1-4612-4484-4_33 Published - 1990

### Publication series

Name Progress in Systems and Control Theory 4

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