Related papers: Ordering and refining path-complete Lyapunov funct…
This paper addresses the critical challenge of developing data-driven certificates for the stability and safety of unmodeled dynamical systems by leveraging a tree data structure and an upper bound of the system's Lipschitz constant.…
We have recently constructed a piecewise quadratic Lyapunov function to prove the boundedness of the reachable values set of piecewise affine discrete-time systems. The method developed also provided an overapproximation of the reachable…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
This paper presents a counterexample-guided iterative algorithm to compute convex, piecewise linear (polyhedral) Lyapunov functions for uncertain continuous-time linear hybrid systems. Polyhedral Lyapunov functions provide an alternative to…
This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the…
Lyapunov stability of a mechanical system means that the dynamic response stays bounded in an arbitrarily small neighborhood of a static equilibrium configuration under small perturbations in positions and velocities. This type of stability…
The objective of the research is to develop a general method of constructing Lyapunov functions for non-linear non-autonomous differential inclusions described by ordinary differential equations with parameters. The goal has been attained…
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…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
In this paper, we consider linear switched systems $\dot x(t)=A_{u(t)} x(t)$, $x\in\R^n$, $u\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\bf UAS} for short). We first…
Safety-critical control of piecewise affine (PWA) systems under bounded additive disturbances requires guarantees not for individual states but for entire state sets simultaneously: a single control action must steer every state in the set…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…
In this note, we propose coordinate-invariant notions of incremental Lyapunov function and provide characterizations of incremental stability in terms of existence of the proposed Lyapunov functions.
The Lyapunov inequality is an indispensable tool for stability analysis in linear control theory. It provides a necessary and sufficient condition for the stability of an autonomous linear-time invariant system in terms of the existence of…
In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…
We present verifiable conditions for synthesizing a single smooth Lyapunov function that certifies both asymptotic stability and safety under bounded controls. These sufficient conditions ensure the strict compatibility of a control barrier…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
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…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
Lyapunov's second or direct method is one of the most widely used techniques for investigating stability properties of dynamical systems. This technique makes use of an auxiliary function, called a Lyapunov function, to ascertain stability…