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Stabilization criteria of a class of switched systems
Author(s) -
Carapito Ana C.
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5688
Subject(s) - mathematics , schur complement , class (philosophy) , block matrix , matrix (chemical analysis) , block (permutation group theory) , algebraic number , complement (music) , lyapunov function , diagonal , pure mathematics , property (philosophy) , control theory (sociology) , combinatorics , mathematical analysis , control (management) , philosophy , materials science , artificial intelligence , chemistry , computer science , composite material , biochemistry , geometry , epistemology , quantum mechanics , eigenvalues and eigenvectors , physics , nonlinear system , complementation , gene , phenotype , management , economics
In this paper, stabilizability property for a switched system under arbitrary switching is considered from an algebraic point of view by means of the existence of a set of block‐diagonal Lyapunov solutions with common Schur complement of certain order—or, equivalently, with common block (1,1)—for the matrix bank. It is shown that the existence of that set is equivalent to the existence of solutions for some Riccati inequalities done in terms of the blocks of matrices of the bank. In addition, we conclude that a particular class of systems with matrix bank constituted by Metzler matrices—Positive Switched Systems—are stabilizable by partial state reset.