Related papers: Real Stability Testing
We establish various certifying determinantal representation results for a polynomial that contains as a factor a prescribed multivariable polynomials that is strictly stable on a tube domain. The proofs use a Cayley transform in…
We consider the stability analysis of feedback systems with rectified linear unit (ReLU) activations, and model this problem with polynomial optimization. Stability can be certified by means of copositive multipliers in the framework of…
P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
In this preliminary work, we propose to use a polynomial approach in order to study the stability of switched systems. The proposed strategy is based on the Bernstein interpolation method that may transform a switched system into a…
We formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix. The limiting…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
This article deals with new polynomial time algorithm for graph isomorphism testing.
We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
The solution of linear inverse problems arising, for example, in signal and image processing is a challenging problem since the ill-conditioning amplifies, in the solution, the noise present in the data. Recently introduced algorithms based…
If K/k is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in K. The algorithm is flexible enough to find factors subject to additional…
Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the…
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…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
This survey revolves around the question how the roots of a monic polynomial (resp. the spectral decomposition of a linear operator), whose coefficients depend in a smooth way on parameters, depend on those parameters. The parameter…