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A Graphical Approach to Prove Contraction of Nonlinear Circuits and Systems

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3 Author(s)
Russo, G. ; Dept. of Syst. & Comput. Eng., Univ. of Naples Federico II, Naples, Italy ; di Bernardo, M. ; Slotine, J.-J.E.

This paper derives a novel approach to prove contraction of nonlinear dynamical systems, based on the use of non-Euclidean norms and their associated matrix measures. A graphical procedure is developed to derive conditions for a system to be contracting. Such conditions can also be used to design control strategies to make a system contracting, or to design consensus and synchronization strategies for networks of nonlinear oscillators. After presenting the main steps of the approach and its proof, both for continuous-time and discrete-time systems, we illustrate the theoretical derivations on a set of representative examples.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:58 ,  Issue: 2 )