2022/11/10 by Ron Ofir, Ofir, Ron, Alexander Ovseevich +3
Engineering · Physics and Astronomy · #Control and Stability of Dynamical Systems #Quantum chaos and dynamical systems #Advanced Thermodynamics and Statistical Mechanics
paper · pdf · doi:10.48550/arxiv.2211.05696
We consider a Lurie system obtained via a connection of a linear time-invariant system and a nonlinear feedback function. Such systems often have more than a single equilibrium and are thus not contractive with respect to any norm. We derive a new sufficient condition for k-contraction of a Lurie system. For k=1, our sufficient condition reduces to the standard stability condition based on the bounded real lemma and a small gain condition. For k=2, our condition guarantees well-ordered asymptotic behaviour of the closed-loop system: every bounded solution converges to an equilibrium, which is not necessarily unique. We apply our results to derive a sufficient condition for k-contractivity of a networked system.