相关论文: Stability of Polytopic Polynomial Matrices
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
We show that for fixed $d>3$ and $n$ growing to infinity there are at least $(n!)^{d-2 \pm o(1)}$ different labeled combinatorial types of $d$-polytopes with $n$ vertices. This is about the square of the previous best lower bounds. As an…
In this paper we study the stability problem of a tree of elastic strings with local Kelvin-Voigt damping on some of the edges. Under the compatibility condition of displacement and strain and continuity condition of damping coefficients at…
We give necessary and sufficient existence criteria, and methods for finding, continuous solutions of linear equations whose coefficients are polynomials.
We give a strongly polynomial time algorithm which determines whether or not a bivariate polynomial is real stable. As a corollary, this implies an algorithm for testing whether a given linear transformation on univariate polynomials…
We give an arithmetic proof of rigidity for postcritically finite polynomials.
A detailed analysis of necessary conditions on a family of many-body potentials, which ensure stability, superstability or strong superstability of a statistical system is given in present work.There has been given also an example of…
This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…
The nonlinear Schr{\"o}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the…
A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$…
We establish several sufficient conditions for the strong ellipticity of any fourth-order elasticity tensor in this paper. The first presented sufficient condition is an extension of positive definite matrices, which states that the strong…
We consider the problem of finding a condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given. It is well known that such conditions can be written as conjunctions of several…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
The Erd\H{o}s-Simonovits stability theorem is one of the most widely used theorems in extremal graph theory. We obtain an Erd\H{o}s-Simonovits type stability theorem in multi-partite graphs. Different from the Erd\H{o}s-Simonovits stability…
A polynomial with rational coefficients is said to be pure with respect to a rational prime $p$ if its Newton polygon has one slope. In this article, we prove that the number of irreducible factors of the $n$-th iterate of a pure polynomial…
In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying its…
For interval polynomial matrices, we identify the minimal testing set, whose stability can guarantee that of the whole uncertain set. Our results improve the conclusions given by Kamal and Dahleh.
In this paper we prove that any degree $d$ deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko's result on Hamiltonian differential…