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Piecewise quadratic Lyapunov functions over conical partitions for robust stability analysis
Author(s) -
Ambrosino Roberto,
Garone Emanuele
Publication year - 2014
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.3206
Subject(s) - quadratic equation , piecewise , lyapunov function , mathematics , piecewise linear function , mathematical optimization , conical surface , stability (learning theory) , class (philosophy) , benchmark (surveying) , computer science , nonlinear system , mathematical analysis , physics , geometry , geodesy , quantum mechanics , artificial intelligence , machine learning , geography
Summary In this paper, the robust stability problem for uncertain linear continuous‐time systems is faced making use of piecewise quadratic Lyapunov functions (PQLF). PQLF are obtained by partitioning the state space into polyhedral cones and by associating a quadratic form with each cone. The proposed formulation allows us to recover, as particular cases of PQLFs, not only the class of quadratic functions but also the class of polyhedral functions. In this way, we manage to show the universality of the class of PQLF for the robust stability problem. The main contribution of the paper is the formulation of a low‐computational cost procedure for the stability analysis of uncertain linear systems. Several numerical examples are included in the paper, where the proposed approach is tested on some benchmark cases taken from the literature. Comparisons with existing methods show that the proposed method performs better under several aspects. Copyright © 2014 John Wiley & Sons, Ltd.