期刊
SYSTEMS & CONTROL LETTERS
卷 54, 期 11, 页码 1131-1134出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sysconle.2005.02.015
关键词
robust stability; parameter dependent Lyapunov function; linear matrix inequalities
In previous works we have proposed a robust stability condition for linear time-invariant discrete-time systems which makes use of a Lyapunov function with linear dependence on the uncertain parameters. This condition is expressed as a set of linear matrix inequalities (LMI) where an additional variable is kept common to all LMI. These features have enabled the development of successful robust filtering and control algorithms. In this short note we investigate possible extensions of this stability condition to handle Lyapunov functions with arbitrary parameter dependence while keeping a variable common to all LMI. By showing that feasibility of the original condition is indeed necessary for the existence of a family of robust stability conditions where the Lyapunov function can have arbitrary dependence on the uncertain parameters, we conclude that no such extensions are possible. (c) 2005 Elsevier B.V. All rights reserved.
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