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L 2 stability, H ∞ control of switched homogeneous nonlinear systems and their semi‐tensor product of matrices representation
Author(s) -
Zhang Lijun,
Zhang Kuize
Publication year - 2013
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.2781
Subject(s) - tensor product , nonlinear system , homogeneous , stability (learning theory) , mathematics , product (mathematics) , control theory (sociology) , representation (politics) , control (management) , pure mathematics , computer science , combinatorics , physics , geometry , artificial intelligence , quantum mechanics , machine learning , politics , political science , law
SUMMARY This paper investigates the problems of L 2 stability and H ∞ control of switched homogeneous nonlinear systems. This paper gives that if a switched homogeneous nonlinear system with disturbance is internally homogeneously asymptotically stable, then it has a finite L 2 gain, and if a switched homogeneous nonlinear system with disturbance and controls is homogeneously stabilizable under the zero disturbance condition, its H ∞ control problem is solvable under some mild conditions, and a homogeneous solution is given. Then, via the semi‐tensor product of matrices method, the aforementioned obtained results are transformed to linear‐like forms, and the aforementioned obtained Hamilton–Jacobi–Isaacs inequality is transformed to a linear‐like matrix inequality, which makes it feasible to compute the solutions by computer. Copyright © 2012 John Wiley & Sons, Ltd.