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This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski…
In this paper we give a new sufficient condition for a general stability of Kronecker coefficients, which we call it additive stability. It was motivated by a recent talk of J. Stembridge at the conference in honor of Richard P. Stanley's…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.
This paper is concerned with the stability problem for the planar linear switched system $\dot x(t)=u(t)A_1x(t)+(1-u(t))A_2x(t)$, where the real matrices $A_1,A_2\in \R^{2\times 2}$ are Hurwitz and $u(\cdot) [0,\infty[\to\{0,1\}$ is a…
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 [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
For a parameter-unknown linear descriptor system, this paper proposes data-driven methods to testify the system's type and controllability and then to stabilize it. First, a data-based condition is developed to identify whether this unknown…
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…
An identification of a spherically symmetric potential by its phase shifts is an important physical problem. Recent theoretical results assure that such a potential is uniquely defined by a sufficiently large subset of its phase shifts at…
This work proposes a mathematical approach that (re)defines a property of Machine Learning models named stability and determines sufficient conditions to validate it. Machine Learning models are represented as functions, and the…
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…
This paper deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to…
A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…
The performance of learning models often deteriorates when deployed in out-of-sample environments. To ensure reliable deployment, we propose a stability evaluation criterion based on distributional perturbations. Conceptually, our stability…
Analyzing system trajectory from the perspective of individual machines provides a distinctive angle to analyze the transient stability of power systems. This two-paper series propose a direct-time-domain method that is based on the…
We consider the problem important for the condensed matter physics, superconductivity physics, and electrodynamics of continuous media - the problem of the matter dielectric permittivity possible values spectrum definition. Two ways of the…
An easy-to-use and effective formula for stability testing of a system with fractional-delay characteristic equation in the general form of $\Delta(s)=P_0(s)+\sum_{i=1}^N P_i(s)\exp(-\zeta_i s^{\beta_i}) =0$, where $P_i(s)$ ($i=0,..., N$)…
In this paper we study the continuous dependence with respect to obstacles for obstacle problems with measure data. This is deeply investigated introducing a suitable type of convergence, which gives stability under very general hypotheses.…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…