Reference : Global stability of relay feedback systems
Scientific congresses, symposiums and conference proceedings : Paper published in a book
Engineering, computing & technology : Multidisciplinary, general & others
http://hdl.handle.net/10993/20476
Global stability of relay feedback systems
English
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > >]
Megretski, A. [> >]
Dahleh, M. A. [> >]
2000
Proceedings of the IEEE American Control Conference (2000 ACC)
IEEE: Institute of Electrical and Electronics Engineers
Volume 1
220 - 224
Yes
0780355202
American Control Conference (2000 ACC)
June 28-30, 2000
Chicago
USA
[en] For a large class of relay feedback systems (RFS) there will be limit cycle oscillations. Conditions to check existence and local stability of limit cycles for these systems are well known. Global stability conditions, however, are practically non-existent. The paper presents conditions in the form of linear matrix inequalities (LMIs) that guarantee global asymptotic stability of a limit cycle induced by a relay with hysteresis in feedback with an LTI stable system. The analysis is based on finding global quadratic Lyapunov functions for a Poincare map associated with the RFS. We found that a typical Poincare map induced by an LTI flow between two hyperplanes can be represented as a linear transformation analytically parametrized by a scalar function of the state. Moreover, level sets of this function are convex. The search for globally quadratic Lyapunov functions is then done by solving a set of LMIs. Most examples of RFS analyzed by the authors were proven globally stable. Systems analyzed include minimum-phase systems, systems of relative degree larger than one, and of high dimension. This leads us to believe that quadratic stability of associated Poincare maps is common in RFS.
http://hdl.handle.net/10993/20476
10.1109/ACC.2000.878837

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