Related papers: Stability Analysis of Planar Probabilistic Piecewi…

In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the…

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…

Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…

This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…

This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…

This paper is concerned with synchronization of complex stochastic dynamical networks in the presence of noise and functional uncertainty. A probabilistic control method for adaptive synchronization is presented. All required probabilistic…

The integration of various power sources, including renewables and electric vehicles, into smart grids is expanding, introducing uncertainties that can result in issues like voltage imbalances, load fluctuations, and power losses. These…

Probabilistic models based on continuous latent spaces, such as variational autoencoders, can be understood as uncountable mixture models where components depend continuously on the latent code. They have proven to be expressive tools for…

This paper considers a Popov type approach to the problem of robust stability for a class of uncertain linear quantum systems subject to unknown perturbations in the system Hamiltonian. A general stability result is given for a general…

A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models…

We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight…

We consider stochastic volatility models using piecewise constant parameters. We suggest a hybrid optimization algorithm for fitting the models to a volatility surface and provide some numerical results. Finally, we provide an outlook on…

We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were…

Ensuring safety through set invariance has proven to be a valuable method in various robotics and control applications. This paper introduces a comprehensive framework for the safe probabilistic invariance verification of both discrete- and…

The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…

Ergodic properties and asymptotic stationarity are investigated in this paper for the pseudo-covariance matrix (PCM) of a recursive state estimator which is robust against parametric uncertainties and is based on plant output measurements…

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…

In this paper, we present a framework for Stability Analysis of Systems of Coupled Linear Partial-Differential Equations. The class of PDE systems considered in this paper includes parabolic, elliptic and hyperbolic systems with Dirichelet,…

Probabilistic and stochastic behavior are omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of fundamental properties of nature, uncertain environments, or simplifications to…