Related papers: Variables Scaling to Solve a Singular Bifurcation …
We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem. The main step is an…
We prove that if a certain entry in the map of the Hadamard-Perron theorem is $T$-periodic in one of the variables, then the stable manifold guaranteed by the Hadamard-Perron theorem is a graph of a $T$-periodic function. As an application,…
We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation, and in which the bifurcation parameter slowly changes in time and is characterized by a sweep…
In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied…
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses…
We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability…
In this paper we present an abstraction algorithm that produces a finite bisimulation quotient for an autonomous discrete-time linear system. We assume that the bisimulation quotient is required to preserve the observations over an…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
Sequences of parametrized Lyapunov equations can be encountered in many application settings. Moreover, solutions of such equations are often intermediate steps of an overall procedure whose main goal is the computation of…
This work proposes a novel distributed framework for verifying the incremental stability of large-scale systems with unknown dynamics and known interconnection structures using graph neural networks. Our proposed approach relies on the…
We present a stability analysis framework for the general class of discrete-time linear switching systems for which the switching sequences belong to a regular language. They admit arbitrary switching systems as special cases. Using recent…
We study products of arbitrary random real $2 \times 2$ matrices that are close to the identity matrix. Using the Iwasawa decomposition of $\text{SL}(2,{\mathbb R})$, we identify a continuum regime where the mean values and the covariances…
We use the backstepping method to study the stabilization of a 1-D linear transport equation on the interval (0, L), by controlling the scalar amplitude of a piecewise regular function of the space variable in the source term. We prove that…
The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…
A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…