Related papers: A sufficient condition for 2-contraction of a feed…
Small-gain conditions used in analysis of feedback interconnections are contraction conditions which imply certain stability properties. Such conditions are applied to a finite or infinite interval. In this paper we consider the case, when…
Relaxed conditions are given for stability of a feedback system consisting of an exponentially stable multi-input multi-output nonlinear plant and an integral controller. Roughly speaking, it is shown that if the composition of the plant…
We consider the problem of making a networked system contracting by designing minimal effort local controllers. Our method combines a hierarchical contraction characterization and a matrix-balancing approach to stabilizing a Metzler matrix…
Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
This paper investigates contraction properties of switched dynamical systems for the case that all modes are non-contracting, thereby extending existing results that require at least one mode to be contracting. Leveraging the property that…
This paper studies the graph-theoretic conditions for stability of positive monotone systems. Using concepts from input-to-state stability and network small-gain theory, we first establish necessary and sufficient conditions for the…
Synchronization of coupled dynamical systems is a widespread phenomenon in both biological and engineered networks, and understanding this behavior is crucial for controlling such systems. Considerable research has been dedicated to…
Many complex systems share two characteristics: 1) they are stochastic in nature, and 2) they are characterized by a large number of factors. At the same time, various natural complex systems appear to have two types of intertwined…
We investigate the dynamics of a limit of interacting FitzHugh-Nagumo neurons in the regime of large interaction coefficients. We consider the dynamics described by a mean-field model given by a nonlinear evolution partial differential…
We address the problem of verifying closed-loop contraction in nonlinear control systems whose controller and contraction metric are both parameterized by neural networks. By leveraging interval analysis and interval bound propagation, we…
We propose easily verifiable necessary and sufficient conditions for the linearizability of two-input systems by an endogenous dynamic feedback with a dimension of at most two.
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
We provide a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a recent small-gain theorem of Angeli and Sontag for monotone systems with…
In this paper, we provide a novel contraction-theoretic approach to analyze two-time scale systems, including those commonly encountered in Online Feedback Optimization (OFO). Our framework endows these systems with several robustness…
We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the…
Many mathematical models of interacting agents assume that individual interactions scale down in proportion to the network size, ensuring that the combined input received from the network does not diverge. In theoretical neuroscience,…
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…
We focus on the long time behavior of complex networks of reaction-diffusion (RD) systems. We prove the existence of the global attractor and a $L^{\infty}$-bound for a network of $n$ RD systems with $d$ variables each. This allows us to…