Related papers: A tropical geometry approach to BIBO stability
The topology of amoebas of complex algebraic hypersurfaces is deeply connected to the combinatorics of the Newton polytope and the convex geometry of the Ronkin function. A long-standing conjecture of Passare and Rullgard asserts that the…
Recently, bipath persistent homology has been proposed as an extension of standard persistent homology, along with its visualization (bipath persistence diagram) and computational methods. In the setting of standard persistent homology, the…
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,…
We study the stability and bifurcation of relative equilibria of a particle on the Lie group $SO(3)$ whose motion is governed by an $SO(3)\times SO(2)$ invariant metric and an $SO(2)\times SO(2)$ invariant potential. Our method is to reduce…
In this paper we study the relative Chow and $K$-stability of toric manifolds in the toric sense. First, we give a criterion for relative $K$-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative…
Numerical computation of the time evolution of the mass transfer rate in a close binary can be and, in particular, has been a computational challenge. Using a simple physical model to calculate the mass transfer rate, we show that for a…
This note deals with Bounded-Input-Bounded-Output (BIBO) stability for semilinear infinite-dimensional dynamical systems allowing for boundary control and boundary observation. We give sufficient conditions that guarantee BIBO stability…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…
The focal point of this paper is to provide some simple and efficient criteria to judge the ${\cal D}$-stability of two families of polynomials, i.e., an interval multilinear polynomial matrix family and a polytopic polynomial family.…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
In this manuscript, we study the stability of the origin for the multivariate geometric Brownian motion. More precisely, under suitable sufficient conditions, we construct a Lyapunov function such that the origin of the multivariate…
The bistable deployable composite boom (Bi-DCB) can achieve bistable function by storing and releasing strain energy, which has a good application prospect in space field. For example, it serves as the main support section of deployable…
We consider a stabilization problem for a piezoelectric system. We prove an exponential stability result under some Lions geometric condition. Our method is based on an identity with multipliers that allows to show an appropriate…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
The stability theorem for persistent homology is a central result in topological data analysis. While the original formulation of the result concerns the persistence barcodes of $\mathbb{R}$-valued functions, the result was later cast in a…
We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…
The theory of persistence, which arises from topological data analysis, has been intensively studied in the one-parameter case both theoretically and in its applications. However, its extension to the multi-parameter case raises numerous…
It is shown that a positive linear system on a time scale with a bounded graininess is uniformly exponentially stable if and only if the characteristic polynomial of the matrix defining the system has all its coefficients positive. Then…
Considerable efforts have been made to analyze the small-signal stability of doubly fed induction generator (DFIG) systems. However, commercial confidentiality and frequency coupling make the DFIG system a grey-box…