Brief paper: State feedback design for input-saturating quadratic systems

Authors:
Giórgio Valmórbida;Sophie Tarbouriech;Germain Garcia
Affiliations:
CNRS, LAAS, 7 Avenue du Colonel Roche, F-31077, Toulouse, France and Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France;CNRS, LAAS, 7 Avenue du Colonel Roche, F-31077, Toulouse, France and Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France;CNRS, LAAS, 7 Avenue du Colonel Roche, F-31077, Toulouse, France and Université de Toulouse, UPS, INSA, INP, ISAE, LAAS, F-31077 Toulouse, France
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

This paper proposes a method to design stabilizing state feedback control laws for nonlinear quadratic systems subject to input saturation. Based on a quadratic Lyapunov function, a modified sector condition and a particular representation for the quadratic terms, synthesis conditions in a ''quasi''-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the state feedback gains maximizing the estimate of the stability region of the closed-loop system.