Related papers: Equilibria and their Stability in Networks with St…
The equilibrium distributions of a Markovian model describing the interaction of several classes of permanent connections in a network are analyzed. It has been introduced by Graham and Robert. For this model each of the connections has a…
In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a…
Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and…
We study networked control of non-linear systems where system states and tentative plant input sequences are transmitted over unreliable communication channels. The sequences are calculated recursively by using a pre-designed nominally…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
We prove that for a wide family of non-uniformly hyperbolic maps and hyperbolic potentials we have equilibrium stability, i.e. the equilibrium states depend continuously on the dynamics and the potential. For this we deduce that the…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
We investigate the stability problem for discrete-time stochastic switched linear systems under the specific scenarios where information about the switching patterns and the probability of switches are not available. Our analysis focuses on…
We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…
We study evolution equations on networks that can be modeled by means of hyperbolic systems. We extend our previous findings in \cite{KraMugNic20} by discussing well-posedness under rather general transmission conditions that might be…
We study the stability and stabilizability of a continuous-time switched control system that consists of the time-invariant $n$-dimensional subsystems \dot{x}=A_ix+B_i(x)u\quad (x\in\mathbb{R}^n, t\in\mathbb{R}_+ \textrm{and}…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to…
This work examines the problem of topology inference over discrete-time nonlinear stochastic networked dynamical systems. The goal is to recover the underlying digraph linking the network agents, from observations of their state-evolution.…
We introduce and solve a general model of dynamic response under external perturbations. This model captures a wide range of systems out of equilibrium including Ising models of physical systems, social opinions, and population genetics.…
Many natural and man-made network systems need to maintain certain patterns, such as working at equilibria or limit cycles, to function properly. Thus, the ability to stabilize such patterns is crucial. Most of the existing studies on…
Stability is a fundamental property of dynamical systems, yet to this date it has had little bearing on the practice of recurrent neural networks. In this work, we conduct a thorough investigation of stable recurrent models. Theoretically,…
Due to the existence of multiple stationary distributions, we study the stability and instability of a stationary distribution for distribution dependent stochastic differential equations. This note is devoted to the instability of a…
Many biological systems, such as metabolic pathways, exhibit bistability behavior: these biological systems exhibit two distinct stable states with switching between the two stable states controlled by certain conditions. Since…
We consider a damped linear hyperbolic system modelling the propagation of pressure waves in a network of pipes. Well-posedness is established via semi-group theory and the existence of a unique steady state is proven in the absence of…