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Improved LMI conditions for gain scheduling and related control problems
Author(s) -
Scorletti Gérard,
Ghaoui Laurent El
Publication year - 1998
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(199808)8:10<845::aid-rnc350>3.0.co;2-i
Subject(s) - gain scheduling , control theory (sociology) , scheduling (production processes) , linear matrix inequality , generality , nonlinear system , computer science , mathematical optimization , dissipative system , skew , scaling , mathematics , control (management) , psychology , telecommunications , physics , geometry , quantum mechanics , artificial intelligence , psychotherapist
The gain scheduling problem considered in this paper concerns a linear system whose state‐space equations depend rationally on real, time‐varying parameters, which are measured in real time. A stabilizing, parameter‐dependent controller is sought, such that a given ℒ 2 ‐gain bound for the closed‐loop system is ensured. Sufficient linear matrix inequality (LMI) conditions are known, that guarantee the existence of such ‘gain‐scheduled’ controllers. This paper improves these results in two directions. First, we show how to exploit the realness of the parameters using a ‘skew‐symmetric scaling’ technique. Moreover, we show how to apply this technique in a time‐varying and/or nonlinear setting. We first devise a general result pertaining to control synthesis of interconnection of dissipative operators, and apply it to the gain‐scheduling problem. Owing to its generality, this result can be applied to other problems such as anti‐windup control, nonlinear control and model reduction. © 1998 John Wiley & Sons, Ltd.