LMI Conditions for $k-\text{contraction}$ Analysis: A Step Towards Design

Recently,
$k-\mathbf{contraction}$
has been proposed as a generalization of contraction properties for nonlinear time-variant systems. Existing tools for
$k-\mathbf{contraction}$
analysis exploit complex mathematical tools known as matrix compounds. This prevented the development of related design methodologies. In this paper, we link
$k-\mathbf{contraction}$
properties to partial stability analysis tools. This leads to new, design-oriented sufficient conditions for
$k-\mathbf{contraction}$
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.