Brief Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

Authors:
Germain Garcia;Bernard Pradin;Sophie Tarbouriech;Fanyou Zeng
Affiliations:
LAAS-CNRS, 7 Avenue du colonel Roche, 31077 Toulouse Cedex 4, France and INSA, 135, Avenue de Rangueil, 31077 Toulouse Cedex 4, France;LAAS-CNRS, 7 Avenue du colonel Roche, 31077 Toulouse Cedex 4, France and INSA, 135, Avenue de Rangueil, 31077 Toulouse Cedex 4, France;LAAS-CNRS, 7 Avenue du colonel Roche, 31077 Toulouse Cedex 4, France;INSA, 135, Avenue de Rangueil, 31077 Toulouse Cedex 4, France
Venue:
Automatica (Journal of IFAC)
Year:
2003

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Abstract

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).