Related papers: Will Random Cone-wise Linear Systems Be Stable?
We reconsider both the global and local stability of solutions of continuously evolving dynamical systems from a geometric perspective. We clarify that an unambiguous definition of stability generally requires the choice of additional…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
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…
The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability with constant coefficients, the problem has a free boundary…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
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…
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…
We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has…
This article concerns the stability of a model for mass-spring systems with positive damping and negative stiness. It is well known that when the coefficients are frozen in time the system is unstable. Here we find conditions on the…
We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
Self-similarity of systems is very popular and intensively developing field during last decades. To this field belong so-called stable distributions and their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an approach to…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We consider the time-dependent nonlinear system $\dot q(t)=u(t)X(q(t))+(1-u(t))Y(q(t))$, where $q\in\R^2$, $X$ and $Y$ are two %$C^\infty$ smooth vector fields, globally asymptotically stable at the origin and $u:[0,\infty)\to\{0,1\}$ is an…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
A tube conveying a large amount of fluid with a free outlet does not sit still. We construct and analyze a nonlinear evolution equation describing such phenomena. Two types of boundary conditions at the inlet are considered, one for which…