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Regulation in bimodal systems
Author(s) -
Wu Zhizheng,
Ben Amara Foued
Publication year - 2007
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/rnc.1270
Subject(s) - control theory (sociology) , parameterized complexity , observer (physics) , stability (learning theory) , closed loop , regulator , computer science , linear system , loop (graph theory) , set (abstract data type) , mathematics , control (management) , control engineering , engineering , algorithm , mathematical analysis , biochemistry , chemistry , physics , quantum mechanics , artificial intelligence , machine learning , gene , programming language , combinatorics
This paper considers the regulation problem for bimodal systems against known disturbance and reference signals. Switching between the two plant models as well as between the disturbance and reference signals is defined according to a switching surface. The design of the proposed regulators involves three main steps. First, a set of observer‐based Q ‐parameterized stabilizing controllers for the switched system is constructed. The stability and the input/output properties for the resulting closed‐loop switched system with the Q ‐parameterized controllers are analysed. Second, regulation conditions for each of the two subsystems in the resulting bimodal switched closed‐loop system are presented. In the third step, regulation conditions for the switched closed‐loop system are developed using two approaches. In the first approach, sufficient regulation conditions are derived based on the closed‐loop system's input–output properties. In the second approach, the forced switched closed‐loop system is transformed into an unforced impulsive switched system using an appropriate coordinate transformation. Hence, the regulation problem for the switched closed‐loop system is transformed into a stability analysis problem for the origin of an impulsive switched system. A regulator synthesis method based on solving some linear matrix inequalities is proposed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.