Related papers: Global Exponential Stability for Complex-Valued Re…
Deep Learning is becoming increasingly relevant in Embedded and Internet-of-things applications. However, deploying models on embedded devices poses a challenge due to their resource limitations. This can impact the model's inference…
Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…
The leader-following consensus problem for general linear multi-agent systems over jointly connected switching networks has been a challenging problem and the solvability of the problem has been limited to the class of linear multi-agent…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…
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…
Recurrent models are a popular choice for video enhancement tasks such as video denoising or super-resolution. In this work, we focus on their stability as dynamical systems and show that they tend to fail catastrophically at inference time…
In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to…
Strong stability, defined by bounds that decay not only over time but also with the number of impulses, has been established as a requirement to ensure robustness properties for impulsive systems with respect to inputs or disturbances. Most…
In this paper, new weighted integral inequalities (WIIs) are first derived by refining the Jensen single and double inequalities. It is shown that the newly derived inequalities in this paper encompass both the Jensen inequality and its…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
This paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems, and establishes the relationship between the eigenvalue distribution and delay-independent stability of neutral…
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…
This paper deals with traveling wavefronts for temporally delayed, spatially discrete reaction-diffusion equations. Using a combination of the weighted energy method and the Green function technique, we prove that all noncritical wavefronts…
In this paper, we analyse the impact of delayed event detection on the stability of a 2-mode planar hybrid automata. We consider hybrid automata with a unique equilibrium point for all the modes, and we find the maximum delay that preserves…
With a small parameter $\epsilon$, Poisson-Nernst-Planck (PNP) systems over a finite one-dimensional (1D) spatial domain have steady state solutions, called 1D boundary layer solutions, which profiles form boundary layers near boundary…
Recent work has shown that topological enhancements to recurrent neural networks (RNNs) can increase their expressiveness and representational capacity. Two popular enhancements are stacked RNNs, which increases the capacity for learning…
Compared with avid research activities of deep convolutional neural networks (DCNNs) in practice, the study of theoretical behaviors of DCNNs lags heavily behind. In particular, the universal consistency of DCNNs remains open. In this…
Recently, there has been a substantial amount of interest in GNN-based anomaly detection. Existing efforts have focused on simultaneously mastering the node representations and the classifier necessary for identifying abnormalities with…
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…