LMI Conditions for $k-\text{contraction}$ Analysis: A Step Towards Design
Samuele Zoboli, Andreu Cecilia, Ulysse Serres, Daniele Astolfi, Vincent Andrieu · 2023
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.