We consider multi-agent systems interacting over directed network topologies where a
subset of agents is adversary/faulty and where the non-faulty agents have the goal of …

We develop two generalizations of contraction theory, namely, semi-contraction and weak-
contraction theory. First, using the notion of seminorm, we propose a geometric framework …

Critical questions in dynamical neuroscience and machine learning are related to the study
of recurrent neural networks and their stability, robustness, and computational efficiency …

The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic
Lyapunov function in the Lur'e problem of absolute stability. A quadratic Lyapunov function …

In this note, we study contractivity of monotone systems and exponential convergence of
positive systems using non-Euclidean norms. We first introduce the notion of conic matrix …

Synchronization of complex networks can easily be seen in nature around us and is an
integral part of many real-world applications. Synchronization of a network is a phenomenon …

Dynamical systems that are contracting on a subspace are said to be semicontracting.
Semicontraction theory is a useful tool in the study of consensus algorithms and dynamical …

We analyze a network of non-identical Rayleigh–van der Pol (RvdP) oscillators
interconnected through either diffusive or nonlinear coupling functions. The work presented …

This entry presents a summarizing overview of the key problems in controlling complex
network systems consisting of ensembles of interacting linear or nonlinear dynamical …

Contraction theory for dynamical systems on Euclidean spaces is well-established. For
contractive (resp. semicontractive) systems, the distance (resp. semidistance) between any …