Robust decoupling of uncertain subsystems

• Published in: International journal of robust and nonlinear control Vol. 32; no. 10; pp. 6086 - 6109
• Main Authors: Baár, Tamás, Luspay, Tamás
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.07.2022
• Subjects: Decoupling; IQC; LFT; Linear matrix inequalities; Linear systems; LMI; Mathematical analysis; Optimization; robust minimum sensitivity; Robustness (mathematics); subsystem decoupling; Subsystems
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6141

The article presents a robust subsystem decoupling framework for uncertain linear systems with linear fractional representation, where the uncertainties are described by Integral Quadratic Constraints. The proposed method relies on the synthesis of input‐ and output transformations, which maximize the robust excitation of a selected subsystem, while minimize this effect on the other parts of the dynamics. More precisely, the notion of minimum gain is defined (and discussed) for uncertain systems, which is then maximized for the targeted subsystem. In order to achieve decoupling, the maximum sensitivity of the undesired dynamical part is minimized simultaneously. These criteria lead to an optimization problem subject to linear matrix inequality constraints, hence can be effectively solved. Numerical examples are used for demonstrating the developed method and its possible applications.