相关论文: Are nonlocal Lagrangian systems fatally unstable?

In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…

This paper examines the local exponential stability (LES) of trajectories for nonlinear systems on Riemannian manifolds. We present necessary and sufficient conditions for LES of a trajectory on a Riemannian manifold by analyzing the…

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be…

Starting from a simple marginally stable model considered for Lyapunov based boundary control of flexible mechanical systems, we add a term driving an instability and prove that for an appropriate control condition the system can become…

The properties of static, spherically symmetric configurations are considered in the framework of two models of nonlocally corrected gravity, suggested in S. Deser and R. Woodard., Phys. Rev. Lett. 663, 111301 (2007), and S. Capozziello et…

Incremental stability is a property of dynamical systems ensuring the uniform asymptotic stability of each trajectory rather than a fixed equilibrium point or trajectory. Here, we introduce a notion of incremental stability for stochastic…

We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…

Recent results have shown the stability of frustration-free Hamiltonians to weak local perturbations, assuming several conditions. In this paper, we prove the stability of free fermion Hamiltonians which are gapped and local. These free…

In this paper, we study the output feedback stabilization for a scalar conservation law with a nonlocal velocity, that models a highly re-entrant manufacturing system as encountered in semi-conductor production. By spectral analysis, we…

Black holes binaries support unstable orbits at very close separations. In the simplest case of geodesics around a Schwarzschild black hole the orbits, though unstable, are regular. Under perturbation the unstable orbits can become the…

We extend the Lyapunov stability criterion to Euler discretizations of differential inclusions. It relies on a pair of Lyapunov functions, one in continuous time and one in discrete time. In the context of optimization, this yields…

In the present article we are interested in further investigations for the barotropic compressible Navier-Stokes system endowed with a non-local capillarity we studied in [7]. Thanks to an accurate study of the associated linear system…

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…

In this paper, we derive an accelerated continuous-time formulation of Adam by modeling it as a second-order integro-differential dynamical system. We relate this inertial nonlocal model to an existing first-order nonlocal Adam flow through…

Negative kinetic energies correspond to ghost degrees of freedom, which are potentially of relevance for cosmology, quantum gravity, and high energy physics. We present a novel wide class of stable mechanical systems where a positive energy…

In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…

This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…

The stability of the recently discovered compacton solutions is studied by means of both linear stability analysis as well as Lyapunov stability criteria. From the results obtained it follows that, unlike solitons, all the allowed compacton…