1. J. L. Mancilla-Aguilar, R. Garcìa, E.D. Sontag, and Y. Wang. On the representation of switched systems with inputs by perturbed control systems. Nonlinear Anal., 60(6):1111-1150, 2005. [PDF] Abstract:

   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.




2. J. L. Mancilla-Aguilar, R. Garcìa, E.D. Sontag, and Y. Wang. Uniform stability properties of switched systems with switchings governed by digraphs. Nonlinear Anal., 63(3):472-490, 2005. [PDF] Abstract:

   This paper develops characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions.

1. J.L. Mancilla-Aguilar, R. Garcìa, E.D. Sontag, and Y. Wang. Representation of switched systems by perturbed control systems. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 3259-3264, 2004.

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