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Sector bounds in stability analysis and control design
Author(s) -
Xia Meng,
Gahinet Pascal,
Abroug Neil,
Buhr Craig,
Laroche Edouard
Publication year - 2020
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.5236
Subject(s) - dissipative system , stability (learning theory) , computer science , robust control , domain (mathematical analysis) , invariant (physics) , mathematical optimization , control theory (sociology) , control (management) , small gain theorem , control system , mathematics , engineering , artificial intelligence , mathematical analysis , physics , quantum mechanics , machine learning , electrical engineering , mathematical physics
Summary The sector stability theorem is an intuitive condition for the stability of feedback loops that unifies many lines of research including robust control and the theory of passive and dissipative systems. Applying this theorem typically requires checking or enforcing sector bounds on linear time‐invariant systems. This article discusses practical and efficient numerical methods for performing these tasks. We derive a frequency‐domain test for sector boundedness and use it to develop O ( n 3 ) numerical algorithms for computing the relative or directional indices of sector bounds. We also discuss how such algorithms can be combined with nonsmooth optimization techniques to enforce sector bounds while designing and tuning controllers. Several application examples illustrate the potential of these tools and techniques.