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Constrained stabilization problems for discrete‐time linear plants
Author(s) -
Saberi Ali,
Shi Guoyong,
Stoorvogel Anton A.,
Han Jian
Publication year - 2004
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.880
Subject(s) - invertible matrix , constraint (computer aided design) , control theory (sociology) , discrete time and continuous time , mathematics , state (computer science) , lti system theory , order (exchange) , contrast (vision) , linear system , invariant (physics) , mathematical optimization , computer science , control (management) , algorithm , pure mathematics , mathematical analysis , economics , statistics , geometry , finance , artificial intelligence , mathematical physics
In this paper we study discrete‐time linear systems with full or partial constraints on both input and state. It is shown that the solvability conditions of stabilization problems are closely related to important concepts, such as the right‐invertibility of the constraints, the location of constraint invariant zeros and the order of constraint infinite zeros. The main results show that for right‐invertible constraints the order of constrained infinite zeros cannot be greater than one in order to achieve global or semi‐global stabilization. This is in contrast to the continuous‐time case. Controllers for both state feedback and measurement feedback are constructed in detail. Issues regarding non‐right invertible constraints are discussed as well. Copyright © 2004 John Wiley & Sons, Ltd.