Related papers: Lyapunov equations: a (fixed) point of view

This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…

Learning controllers merely based on a performance metric has been proven effective in many physical and non-physical tasks in both control theory and reinforcement learning. However, in practice, the controller must guarantee some notion…

Here, we study the ultimately bounded stability of network of mismatched systems using Lyapunov direct method. The upper bound on the error of oscillators from the center of the neighborhood is derived. Then the performance of an adaptive…

While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…

We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…

This paper includes results centered around three topics, all of them related with the nonlinear stability of equilibria in Poisson dynamical systems. Firstly, we prove an energy-Casimir type sufficient condition for stability that uses…

In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis…

Fixed points represent equilibrium states, stability, and solutions to a range of problems. It has been an active field of research. In this paper, we provide an overview of the main branches of fixed point theory. We discuss the key…

This work is devoted to prove the pointwise controllability of the Bernoulli-Euler beam equation. It is obtained as a limit of internal controllability of the same type of equation.

In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more…

This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…

Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws…

We present a true-dynamics-agnostic, statistically rigorous framework for establishing exponential stability and safety guarantees of closed-loop, data-driven nonlinear control. Central to our approach is the novel concept of conformal…

While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…

This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port--Hamiltonian systems including second order models such as the Euler--Bernoulli beam. The control design is achieved using…

Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in…

Copositive linear Lyapunov functions are used along with dissipativity theory for stability analysis and control of uncertain linear positive systems. Unlike usual results on linear systems, linear supply-rates are employed here for…

In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…

Various controllability conditions have been obtained by researchers for heterogeneous networked systems with linear dynamics. However, the literature for nonlinear, heterogeneous networked systems is comparatively less. In this paper we…