Related papers: Strong Lyapunov functions for rough systems
We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of…
This work presents an approach to synthesize a Lyapunov-like function to ensure incrementally input-to-state stability ($\delta$-ISS) property for an unknown discrete-time system. To deal with challenges posed by unknown system dynamics, we…
We consider additive functionals of stationary Markov processes and show that under Kipnis-Varadhan type conditions they converge in rough path topology to a Stratonovich Brownian motion, with a correction to the Levy area that can be…
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…
We prove the existence of random attractors for a large class of degenerate stochastic partial differential equations (SPDE) perturbed by joint additive Wiener noise and real, linear multiplicative Brownian noise, assuming only the standard…
We prove the stability of the critical hypersurfaces associated with the three-dimensional general relativistic Poynting-Robertson effect. The equatorial ring configures to be as a stable attractor and the whole critical hypersurface as a…
For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal…
Motivated by robust and quantile regression problems, we investigate the stochastic gradient descent (SGD) algorithm for minimizing an objective function $f$ that is locally strongly convex with a sub--quadratic tail. This setting covers…
We numerically study in the one-dimensional case the validity of the functional calculated by Graham and coworkers as a Lyapunov potential for the Complex Ginzburg-Landau equation. In non-chaotic regions of parameter space the functional…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Algorithms increasingly operate within complex physical, social, and engineering systems where they are exposed to disturbances, noise, and interconnections with other dynamical systems. This article extends known convergence guarantees of…
This work investigates the long-term distributional behavior of the reversible Selkov lattice systems defined on the set $\mathbb{Z}$ and driven by locally Lipschitz \emph{L\'{e}vy noises}, which possess two pairs of oppositely signed…
In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further…
Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical…
In this study, we propose new global stabilization approaches for a class of polynomial systems in both model-based and data-driven settings. The existing model-based approach guarantees global asymptotic stability of the closed-loop system…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…
Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics. We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
We give a succinct and self-contained description of the synchronized motion on networks of mutually coupled oscillators. Usually, the stability criterion for the stability of synchronized motion is obtained in terms of Lyapunov exponents.…
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…