Singular ℋ︁ 2  control of discrete‐time systems: From frequency to time domain | Zendy

Stefanovski Jovan | Zendy

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Singular ℋ︁ 2 control of discrete‐time systems: From frequency to time domain

Author(s) -

Stefanovski Jovan

Publication year - 2009

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.1559

Subject(s) - control theory (sociology) , decoupling (probability) , discrete time and continuous time , realization (probability) , observer (physics) , mathematics , transfer matrix , controller (irrigation) , matrix (chemical analysis) , frequency domain , stability (learning theory) , state (computer science) , time domain , control (management) , computer science , control engineering , mathematical analysis , engineering , algorithm , agronomy , statistics , physics , materials science , quantum mechanics , artificial intelligence , machine learning , composite material , computer vision , biology

Necessary and sufficient conditions for the existence of a minimizing discrete‐time ℋ 2 control, when assumptions are the internal stabilizability and left‐ and right‐invertibility of transfer matrices G 12 and G 21 , are presented. Unlike the existing approach with a transformation into a disturbance decoupling problem with a measurement feedback and internal stability, we use a direct approach: from frequency to time domain. The first main result gives a necessary and sufficient existence condition for ℋ 2 control: that a minimal realization of the infimal controller is stabilizing. The second main result presents a realization of an optimal controller that has a state observer form, identical to the form of the regular case, except that the state‐feedback gain matrix and the observer gain matrix are replaced by some stabilizing matrices. Copyright © 2009 John Wiley & Sons, Ltd.

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