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H ∞ Control with Transients for Singular Systems
Author(s) -
Feng Zhiguang,
Lam James,
Xu Shengyuan,
Zhou Shaosheng
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1163
Subject(s) - control theory (sociology) , mathematics , measure (data warehouse) , norm (philosophy) , attenuation , scalar (mathematics) , singular value , controller (irrigation) , control (management) , computer science , physics , eigenvalues and eigenvectors , agronomy , geometry , optics , quantum mechanics , database , artificial intelligence , political science , law , biology
In this paper, the problem of a generalized type of H ∞ control is investigated for continuous‐time singular systems, which treats a mixed attenuation of exogenous inputs and initial conditions. First, a performance measure that is essentially the worst‐case norm of the regulated outputs over all exogenous inputs and initial conditions is introduced. A necessary and sufficient condition is obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Based on the criterion a sufficient condition for the existence of a state‐feedback controller is established in terms of linear matrix inequalities. Moreover, the relationship between the performance measure and the standard H ∞ norm of the system is provided. Two numerical examples are given to demonstrate the properties of the obtained results.