Related papers: Stability estimates for adaptive focused time-freq…
We deal with the stability issue for the determination of outgoing time-harmonic acoustic waves from their far-field patterns. We are especially interested in keeping as explicit as possible the dependence of our stability estimates on the…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
Evaluating robustness under temporal distribution shift remains an open challenge. Existing metrics quantify the average decline in performance, but fail to capture how models adapt to evolving data. As a result, temporal degradation is…
We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…
High-resolution time-frequency (TF) analysis plays crucial role in characterizing multicomponent signal (MCSs) and estimating oscillatory properties. Linear time-frequency representations (TFRs) such as classical short-time Fourier…
The present paper provides a sufficient condition to ensure output finite-time and fixed-time stability. Comparing with analogous researches the proposed result is less restrictive and obtained for a wider class of systems. The presented…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
The analysis of non-stationary signals in non-uniformly sampled data is a challenging task. Time-integrated methods, such as the generalised Lomb-Scargle (GLS) periodogram, provide a robust statistical assessment of persistent periodicities…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method…
The paper deals with the problem of the sampled data feedback stabilization for autonomous nonlinear systems. The corresponding results extend those obtained in earlier works by the same authors. The sufficient conditions we establish are…
Frequency Estimation of a complex exponential is a problem relevant to a large number of fields. In this paper a computationally efficient and accurate frequency estimator is presented using the guaranteed stable Sliding DFT which gives…
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…
This paper focuses on the mathematical approaches to the analysis of stability that is a crucial step in the design of dynamical systems. Three methods are presented, namely, absolutely integrable impulse response, Fourier integral, and…
We develop a novel continuous-time asymptotic framework for inference on whether the predictive ability of a given forecast model remains stable over time. We formally define forecast instability from the economic forecaster's perspective…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
Transformers have shown great power in time series forecasting due to their global-range modeling ability. However, their performance can degenerate terribly on non-stationary real-world data in which the joint distribution changes over…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…