Related papers: A tropical geometry approach to BIBO stability
Let X be a Fano manifold. G.Tian proves that if X admits a Kaehler-Einstein metric, then it satisfies two different stability conditions: one involving the Futaki invariant of a special degeneration of X, the other Hilbert-Mumford-stability…
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…
We present a simple feedback description of parametric instabilities which can be applied to a variety of optical systems. Parametric instabilities are of particular interest to the field of gravitational-wave interferometry where high…
In this paper we characterize the stabilization for some thermo-elastic type system with Cattaneo law and we prove that the exponential or polynomial stability of this system implies a polynomial stability of the correspond thermoelastic…
We consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
Cell-fate transition can be modeled by ordinary differential equations (ODEs) which describe the behavior of several molecules in interaction, and for which each stable equilibrium corresponds to a possible phenotype (or 'biological…
The stability radius for finitely many interconnected linear exponentially stable well-posed systems with respect to static perturbations is studied. If the output space of each system is finite-dimensional, then a lower bound for the…
In this paper, we first consider the well-posedness and asymptotic behavior of a one-dimensional piezoelectric beam system with control boundary conditions of fractional derivative type, which represent magnetic effects on the system. By…
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…
A polynomial $f(x)$ over a field $K$ is called stable if all of its iterates are irreducible over $K$. In this paper we study the stability of trinomials over finite fields. Specially, we show that if $f(x)$ is a trinomial of even degree…
We prove the existence of explicit linear multistep methods of any order with positive coefficients. Our approach is based on formulating a linear programming problem and establishing infeasibility of the dual problem. This yields a number…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: ``Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the…
We develop an iterative technique for computing the unstable and stable eigenfunctions of the invariant tori of diffeomorphisms. Using the approach of Jorba, the linearized equations are rewritten as a generalized eigenvalue problem.…
In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time…
We study Fayet-Iliopoulos (FI) terms of six-dimensional supersymmetric Abelian gauge theory compactified on a $T^2/Z_2$ orbifold. Such orbifold compactifications can lead to localized FI-terms and instability of bulk zero modes. We study…
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…
The calculation of the transfer matrix for a large non-periodic multilayered system may become unstable in the presence of absorption. We discuss the origin of this instability and we explore two methods to overcome it: the use of a total…
This paper provides a necessary and sufficient condition for guaranteeing exponential stability of the linear difference equation $x(t)=Ax(t-a)+Bx(t-b)$ where $a>0,b>0$ are constants and $A,B$ are $n\times n$ square matrices, in terms of a…