State feedback design for input-saturating quadratic systems

• Published in: Automatica (Oxford) Vol. 46; no. 7; pp. 1196 - 1202
• Main Authors: Valmórbida, Giórgio, Tarbouriech, Sophie, Garcia, Germain
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.07.2010; Elsevier
• Subjects: Applied sciences; Automatic; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control systems; Control theory. Systems; Design engineering; Engineering Sciences; Exact sciences and technology; Gain; Input saturations; Local stability; Lyapunov functions; Optimization; Quadratic systems; Representations; Saturation; State feedback; Input saturations; Quadratic systems; Local stability; State feedback; Control program; Non linear control; Feedback regulation; Control synthesis; Input saturation; Stability region; Non linear system; Quadratic system; Local effect; Optimization; Closed feedback; Linear matrix inequality; Lyapunov function; Quadratic function
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.03.016

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.