Related papers: Stability of the \`A Trous Algorithm Under Iterati…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
This paper explores the fundamental limits of a simple system, inspired by the intermittent Kalman filtering model, where the actuation direction is drawn uniformly from the unit hypersphere. The model allows us to focus on a fundamental…
Striped Turing patterns and solitary band and disk structures are constructed using a three-variable multiscale model with cubic nonlinearity and global control. The existence and stability conditions of regular structures are analysed…
This paper addresses two interrelated problems of the nonlinear filtering mechanism and fast attitude filtering with the matrix Fisher distribution (MFD) on the special orthogonal group. By analyzing the distribution evolution along Bayes'…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
We consider the conceptual two-layered oscillating tank of Inoue & Smyth (2009), which mimics the time-periodic parallel shear flow generated by low-frequency (e.g. semi-diurnal tides) and small-angle oscillations of the density interface.…
We investigate the linear stability of a flat interface that separates a liquid layer from a fully-developed turbulent gas flow. In this context, linear-stability analysis involves the study of the dynamics of a small-amplitude wave on the…
This article provides a characterization of stability for switched nonlinear systems under average dwell-time constraints, in terms of necessary and sufficient conditions involving multiple Lyapunov functions. Earlier converse results focus…
In this paper, we discuss the Hyers-Ulam stability of closable (unbounded) operators with several interesting examples. We also present results pertaining to the Hyers-Ulam stability of the sum and product of closable operators to have the…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that…
The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP…
The \v{C}ech and Rips constructions of persistent homology are stable with respect to perturbations of the input data. However, neither is robust to outliers, and both can be insensitive to topological structure of high-density regions of…
The phenomenon of stable persistent currents is central to the studies of superfluidity in a range of physical systems. While all of the previous theoretical studies of superfluid flows in annular geometries concentrated on conservative…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
We consider a single-server cyclic polling system with three queues where the server follows an adaptive rule: if it finds one of queues empty in a given cycle, it decides not to visit that queue in the next cycle. In the case of limited…