On Uniform Stabilization of Discrete-Time Linear Parameter-Varying Control Systems

For discrete-time polytopic linear parameter-varying systems, the uniform exponential stability, which is equivalent to the asymptotic stability and includes the quadratic stability as a special case, is characterized by the union of an increasing family of linear matrix inequality conditions. On th...

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Bibliographic Details
Published in:	IEEE transactions on automatic control Vol. 51; no. 10; pp. 1714 - 1721
Main Author:	LEE, Ji-Woong
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01-10-2006 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Applied sciences Asymptotic properties Asymptotic stability Computer science; control theory; systems Control system analysis Control system synthesis Control systems Control theory. Systems Controllers Discrete linear inclusion Equivalence Exact sciences and technology Linear matrix inequalities linear matrix inequality (LMI) linear parameter-varying (LPV) system Linear systems Lyapunov method Mathematical analysis output injection Robustness Stability State feedback Time varying systems Uncertainty Unions Polytope State feedback Finite memory Stabilization Control synthesis Linear parameter varying system linear matrix inequality (LMI) Non conservative system Exponential stability linear parameter-varying (LPV) system Asymptotic stability Time varying system Discrete time Linear matrix inequality output injection Discrete linear inclusion
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Summary:	For discrete-time polytopic linear parameter-varying systems, the uniform exponential stability, which is equivalent to the asymptotic stability and includes the quadratic stability as a special case, is characterized by the union of an increasing family of linear matrix inequality conditions. On the other hand, in certain cases, nonconservative synthesis of uniformly stabilizing controllers is achieved via a system of finite number of linear matrix inequalities if the controller is allowed to have finite memory of past parameters. Two such cases are robust state feedback (in a relaxed sense) against polytopic parameter variations, and multiple output injections under polytopic fusion rules
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0018-9286 1558-2523
DOI:	10.1109/TAC.2006.880804