Abstract
A Lurie system is the interconnection of a linear time-invariant system and a nonlinear feedback function. 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. However, Lurie systems often have more than a single equilibrium and are thus not contractive with respect to any norm. For k=2, our condition guarantees a well-ordered asymptotic behavior of the closed-loop system: every bounded solution converges to an equilibrium, which is not necessarily unique. We demonstrate our results by deriving a sufficient condition for k-contraction of a general networked system, and then applying it to guarantee k-contraction in a Hopfield neural network, a nonlinear opinion dynamics model, and a 2-bus power system.
Original language | English |
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Article number | 111341 |
Journal | Automatica |
Volume | 159 |
DOIs | |
State | Published - Jan 2024 |
Keywords
- Bounded real lemma
- Contraction theory
- Stability of nonlinear systems
- k-compound matrices
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Electrical and Electronic Engineering