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A method to construct (strict) Lyapunov Functions for a class of Higher Order Sliding Modes (HOSM) algorithms, that are homogeneous and piecewise state affine is presented. It is shown first that several HOSM algorithms presented in the literature posses these properties. The basic idea of the construction method is borrowed from the constructive proofs of the Lyapunov's Converse Theorems. It is shown,...
Canonical labelling of graphs (CL, for short) can be used, e.g., to test isomorphism. We prove that a simple vertex classification procedure results after only two refinement steps in a CL of random graphs with probability 1 - exp(-cn). With a slight modification we obtain a linear time CL algorithm with only exp(-cn log n/log log n) probability of failure. An additional depth-first search yields...
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