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A team algorithm for robust stability analysis and control design of uncertain time‐varying linear systems using piecewise quadratic Lyapunov functions
Author(s) -
Almeida H. L. S.,
Bhaya A.,
Falcão D. M.,
Kaszkurewicz E.
Publication year - 2001
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.558
Subject(s) - piecewise , mathematics , linear matrix inequality , mathematical optimization , lyapunov function , convex optimization , interior point method , stability (learning theory) , piecewise linear function , quadratic equation , robust control , regular polygon , nonlinear system , computer science , mathematical analysis , physics , geometry , quantum mechanics , machine learning
A team algorithm based on piecewise quadratic simultaneous Lyapunov functions for robust stability analysis and control design of uncertain time‐varying linear systems is introduced. The objective is to use robust stability criteria that are less conservative than the usual quadratic stability criterion. The use of piecewise quadratic Lyapunov functions leads to a non‐convex optimization problem, which is decomposed into a convex subproblem in a selected subset of decision variables, and a lower‐dimensional non‐convex subproblem in the remaining decision variables. A team algorithm that combines genetic algorithms (GA) for the non‐convex subproblem and interior‐point methods for the solution of linear matrix inequalities (LMI), which form the convex subproblem, is proposed. Numerical examples are given, showing the advantages of the proposed method. Copyright © 2001 John Wiley & Sons, Ltd.