Robust Control for Continuous LPV System with Restricted-Model-Based Control

• Published in: Circuits, systems, and signal processing Vol. 36; no. 6; pp. 2499 - 2520
• Main Authors: Maalej, Sonia, Kruszewski, Alexandre, Belkoura, Lotfi
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2017; Springer Nature B.V; Springer Verlag
• Subjects: Automatic; Automatic Control Engineering; Circuits and Systems; Computer Science; Control systems; Controllers; Derivatives; Dynamical systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Engineering Sciences; Generalized linear models; Instrumentation; Matrix; Nonlinear systems; Parameters; Searching; Short Paper; Signal,Image and Speech Processing; Stabilization; Transformations; Robust control; Linear matrix inequalities; Polytopic systems; Nonlinear systems
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-016-0404-6

This paper deals with the robust stabilization of a class of linear parameter varying systems in the continuous control case. Instead of using a state observer or searching for a dynamic output feedback, the considered controller is based on output derivative estimation. This allows the stabilization of the plant with very large parameter variation or uncertainties. The robustness of such controller, for any all-poles single-input/single-output system, is provided for second- and third-order plants. The proof of stability is based on the polytopic representation of the closed loop under Lyapunov conditions and system transformations. The result is a control structure with only one parameter tuned via very simple conditions.