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Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method
Author(s) -
Wang Peng,
Zhao Jun
Publication year - 2019
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.4552
Subject(s) - dissipative system , control theory (sociology) , constraint (computer aided design) , mathematics , stability (learning theory) , function (biology) , scheme (mathematics) , set (abstract data type) , linear programming , control (management) , linear system , state (computer science) , exponential stability , computer science , mathematical optimization , nonlinear system , mathematical analysis , algorithm , physics , geometry , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology , programming language
Summary In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.