Observer-Based H∞ Control for One-Sided Lipschitz Nonlinear Systems with Uncertain Input Matrix

• Published in: Circuits, systems, and signal processing Vol. 41; no. 3; pp. 1406 - 1425
• Main Authors: Salehifar, Homa, Shahbazzadeh, Majid, Sadati, Seyed Jalil
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2022; Springer Nature B.V
• Subjects: Applied mathematics; Circuits and Systems; Computer engineering; Control systems design; Control theory; Design; Electrical Engineering; Electronics and Microelectronics; Engineering; H-infinity control; Instrumentation; Lipschitz condition; Nonlinear systems; Signal processing; Signal,Image and Speech Processing; Uncertainty; control; Linear matrix inequalities; One-sided Lipschitz systems; Parametric uncertainties; Observer-based control
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-021-01847-x

This paper investigates the problem of observer-based H ∞ control for one-sided Lipschitz nonlinear systems subject to parametric uncertainties and external disturbances. In order to relax some conservatisms and limitations of the traditional Lipschitz condition, the one-sided Lipschitz and quadratically inner-bounded conditions are used. On the contrary to the methods proposed in the literature, our method allows for uncertainty in the input matrix B , as well as the dynamic and output matrices A and C . To derive design conditions in terms of LMIs, the well-known Young’s relation is employed for handling the bilinear terms naturally arising in observer-based controller design. Finally, two examples are presented to demonstrate the validity of the theoretical results.