Related papers: A relaxed small-gain theorem for infinite networks
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…
This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
We are concerned with input-to-state stability (ISS) of randomly switched systems. We provide preliminary results dealing with sufficient conditions for stochastic versions of ISS for randomly switched systems without control inputs, and…
In this paper, we present a novel approach to identify the generators and states responsible for the small-signal stability of power networks. To this end, the newly developed notion of information transfer between the states of a dynamical…
This paper deals with the analysis of input/output-to-state stability (IOSS) and construction of state-norm estimators for continuous-time switched nonlinear systems under restricted switching. Our contributions are twofold. First, given a…
This paper examines small-signal stability of electrical networks composed dominantly of three-phase grid-following inverters. We show that the mere existence of a high-voltage power flow solution does not necessarily imply small-signal…
The usual passivity theorem considers a closed-loop, the direct chain of which consists of a strictly passive stable operator $H_{1}$, and the feedback chain of which consists of a passive operator $H_{2}$. Then the closed-loop is stable.…
This paper studies the effect of perturbations on the gradient flow of a general nonlinear programming problem, where the perturbation may arise from inaccurate gradient estimation in the setting of data-driven optimization. Under suitable…
This paper presents reduction theorems for stability, attractivity, and asymptotic stability of compact subsets of the state space of a hybrid dynamical system. Given two closed sets $\Gamma_1 \subset \Gamma_2 \subset \Re^n$, with…
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…
The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual…
Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from…
Exact discrete-time models of nonlinear systems are difficult or impossible to obtain, and hence approximate models may be employed for control design. Most existing results provide conditions under which the stability of the approximate…
According to the May-Wigner stability theorem, increasing the complexity of a network inevitably leads to its destabilization, such that a small perturbation will be able to disrupt the entire system. One of the principal arguments against…
This paper studies the problem of coordinating a group of $n$th-order integrator systems. As for the well-studied conventional consensus problem, we consider linear and distributed control with only local and relative measurements. We…
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 deals with input/output-to-state stability (IOSS) of switched nonlinear systems in the discrete-time setting. We present an algorithm to construct periodic switching signals that obey pre-specified restrictions on admissible…
In this paper, we investigate well-posedness and stability properties of distributed parameter systems, with particular emphasis on linear positive control systems. We establish a characterization of the well-posedness in the Banach lattice…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…