LMI conditions for k-contraction analysis: a step towards design
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Abstract
Recently, k-contraction has been proposed as a generalization of contraction properties for nonlinear time-variant systems. Existing tools for k-contraction analysis exploit complex mathematical tools known as matrix compounds. This prevented the development of related design methodologies. In this paper, we link k-contraction properties to partial stability analysis tools. This leads to new, design-oriented sufficient conditions for k-contraction analysis which do not involve matrix compounds. We also show that such sufficient conditions are necessary for the linear time-invariant framework. Finally, we compare our results to existing methods and highlight their advantages.
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