Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 60, Issue 6, Pages 1111-1150Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2004.10.012
Keywords
switched systems; differential inclusions; relaxation theorems; input-to-state stability; Lyapunov method
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This paper provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems. The control systems have dynamics given by differential equations, and their inputs consist of the original controls together with disturbances that evolve in compact sets; their sets of maximal trajectories contain, as a dense subset, the set of maximal trajectories of the original system. Several applications to control theory, dealing with properties of stability with respect to inputs and of detectability, are derived as a consequence of the representation theorem. (C) 2004 Elsevier Ltd. All rights reserved.
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