Related papers: Stability Analysis for Stochastic Hybrid Inclusion…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
The paper introduces sufficient conditions for input-to-state stability (ISS) of a class of impulsive systems with jump maps that depend on time. Such systems can naturally represent an interconnection of several impulsive systems with…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
We construct a generic, simple, and efficient scheduling policy for stochastic processing networks, and provide a general framework to establish its stability. Our policy is randomized and prioritized: with high probability it prioritizes…
In many computational tasks and dynamical systems, asynchrony and randomization are naturally present and have been considered as ways to increase the speed and reduce the cost of computation while compromising the accuracy and convergence…
We study limit theorems for partial sums of instantaneous functions of a homogeneous Markov chain on a general state space. The summands are heavy-tailed and the limits are stable distributions. The conditions imposed on the transition…
We present a detailed analysis of non-degenerate time-homogeneous It\^o-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability…
Motivated by the lack of a suitable constructive framework for analyzing popular stochastic models of Systems Biology, we devise conditions for existence and uniqueness of solutions to certain jump stochastic differential equations (SDEs).…
This paper discusses the stability analysis of linear parameter varying systems with a parameter-dependent delay where the parameters are assumed to be stochastic piecewise constants under spontaneous Poissonian jumps. Based on stochastic…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
Neural-based, data-driven analysis and control of dynamical systems have been recently investigated and have shown great promise, e.g. for safety verification or stability analysis. Indeed, not only do neural networks allow for an entirely…
Hybrid systems - more precisely, their mathematical models - can exhibit behaviors, like Zeno behaviors, that are absent in purely discrete or purely continuous systems. First, we observe that, in this context, the usual definition of…
In high-dimensional learning, models remain stable until they collapse abruptly once the sample size falls below a critical level. This instability is not algorithm-specific but a geometric mechanism: when the weakest Fisher eigendirection…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Understanding under what conditions populations, whether they be plants, animals, or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…
We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…