Related papers: Weak instability of Hamiltonian equilibria
For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
In the presence of noncompact symmetry, the stability of relative equilibria under momentum-preserving perturbations does not generally imply robust stability under momentum-changing perturbations. For axisymmetric relative equilibria of…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies…
In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
This work is to investigate the (top) Lyapunov exponent for a class of Hamiltonian systems under small non-Gaussian L\'evy noise. In a suitable moving frame, the linearisation of such a system can be regarded as a small perturbation of a…
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria, weak equilibria and strong equilibria. The discount function is assumed to be log sub-additive and the…
In 2002, Fatiha Alabau, Piermarco Cannarsa and Vilmos Komornik investigated the extent of asymptotic stability of the null solution for weakly coupled partially damped equations of the second order in time. The main point is that the…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the…
We study the (weak) equilibrium problem arising from the problem of optimally stopping a one-dimensional diffusion subject to an expectation constraint on the time until stopping. The weak equilibrium problem is realized with a set of…
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
Purely rotational relative equilibria of an ellipsoidal underwater vehicle occur at nongeneric momentum where the symplectic reduced spaces change dimension. The stability these relative equilibria under momentum changing perturbations is…
We devise a generalisation of the energy momentum-method for studying the stability of non-autonomous Hamiltonian systems with a Lie group of Hamiltonian symmetries. A generalisation of the relative equilibrium point notion to a…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…