Journal
SYSTEMS & CONTROL LETTERS
Volume 55, Issue 1, Pages 52-61Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2005.05.003
Keywords
robust stability; homogeneous polynomially parameter-dependent Lyapunov function; linear matrix inequality; continuous and discrete-time uncertain systems; time-invariant uncertainty
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The robust stability of uncertain linear systems in polytopic domains is investigated in this paper. The main contribution is to provide a systematic procedure for generating sufficient robust stability linear matrix inequality conditions based on homogeneous polynomially parameter-dependent Lyapunov matrix functions of arbitrary degree on the uncertain parameters. The conditions exploit the positivity of the uncertain parameters, being constructed in such a way that: as the degree of the polynomial increases, the number of linear matrix inequalities and free variables increases and the test becomes less conservative; if a feasible solution exists for a certain degree, the conditions will also be verified for larger degrees. For any given degree, the feasibility of a set of linear matrix inequalities defined at the vertices of the polytope assures the robust stability. Both continuous and discrete-time uncertain systems are addressed, as illustrated by numerical examples. (c) 2005 Elsevier B.V. All rights reserved.
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