Related papers: Deep Lyapunov Function: Automatic Stability Analys…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
The stability of the zero solution of a nonlinear Caputo fractional differential equation with noninstantaneous impulses is studied using Lyapunov like functions. The novelty of this paper is based on the new definition of the derivative of…
Inspired by the widespread concept of Lyapunov-Krasovskii functionals of complete type, this article proposes an alternative class of functionals, termed Lyapunov-Krasovskii functionals of robust type. Their construction aims at improving…
Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging…
Machine learning techniques have demonstrated their effectiveness in achieving autonomy and optimality for nonlinear and high-dimensional dynamical systems. However, traditional black-box machine learning methods often lack formal stability…
An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof are presented in details for the case of systems with multiple delays. The state of the art, ongoing…
The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side…
Out of the recent advances in systems and control (S\&C)-based analysis of optimization algorithms, not enough work has been specifically dedicated to machine learning (ML) algorithms and its applications. This paper addresses this gap by…
The property that every control system should posses is stability, which translates into safety in real-life applications. A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions…
We present a stability analysis of the standard nonautonomous systems type for a recently introduced generalized Lane-Emden equation which is shown to explain the presence of some of the structures observed in the atomic spatial…
Aiming at the difficulty of stability analysis in practical application of existing control methods, a controller strategy based on lyapunov stability theory is proposed to realize stable control for any control method. In order to…
In 2002, Fatiha Alabau, Piermarco Cannarsa and Vilmos Komornik investigated the extent of asymptotic stability of the null solution for weakly coupled partially damped equations of the second order in time. The main point is that the…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed…
Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness…
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…