Related papers: Stability of the \`A Trous Algorithm Under Iterati…
This paper examines the frame properties of finitely and infinitely iterated dyadic filter banks. It is shown that the stability of an infinitely iterated dyadic filter bank guarantees that of any associated finitely iterated dyadic filter…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. 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…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…
Graph-structured data arise in a variety of real-world context ranging from sensor and transportation to biological and social networks. As a ubiquitous tool to process graph-structured data, spectral graph filters have been used to solve…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
When is a nonlinear filter stable with respect to its initial condition? In spite of the recent progress, this question still lacks a complete answer in general. Currently available results indicate that stability of the filter depends on…
A stable filter has the property that it asymptotically `forgets' initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
In this paper, we study the stability of commonly used filtration functions in topological data analysis under small perturbations of the underlying nonrandom point cloud. Relying on these stability results, we then develop a test procedure…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
This paper addresses the stability analysis of infinite-dimensional sampled-data systems under unbounded perturbations. We present two classes of unbounded perturbations preserving the exponential stability of sampled-data systems. To this…
Recent years have bore witness to the proliferation of distributed filtering techniques, where a collection of agents communicating over an ad-hoc network aim to collaboratively estimate and track the state of a system. These techniques…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
Recently, the stability of graph filters has been studied as one of the key theoretical properties driving the highly successful graph convolutional neural networks (GCNs). The stability of a graph filter characterizes the effect of…
We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input…
A new result on stability of an optimal nonlinear filter with respect to small perturbations on every step is established.
This work establishes rigorous, novel and widely applicable stability guarantees and transferability bounds for graph convolutional networks -- without reference to any underlying limit object or statistical distribution. Crucially,…
This paper presents stability and accuracy analysis of a high-order explicit time stepping scheme introduced by \cite[Section 2.2]{Buvoli2019}, which exhibits superior stability compared to classical Adams-Bashforth. A conjecture that is…