Related papers: Local nonsmooth Lyapunov pairs for first-order evo…
Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the…
This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…
A simple example that I have been requested illustrates the statement in E-print nlin.CD/0201060 that solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropriate time-dependent…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…
The initial-boundary value problems for linear non-autonomous first order evolution equations are examined. Our assumptions provide a unified treatment which is applicable to many situations, where the domains of the operators may change…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
This paper studies the continuous-time dynamics of primal-dual algorithms for linearly constrained convex optimization problems and provides a quantitative convergence analysis using the Lyapunov functions. With the growing prevalence of…
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
We prove some new results regarding the boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may contain time-dependent…
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 presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property,…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
We consider the typical behaviour of random dynamical systems of order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at the endpoints. Our study removes any requirement for continuous differentiability save…
In this paper we employ SMT solvers to soundly synthesise Lyapunov functions that assert the stability of a given dynamical model. The search for a Lyapunov function is framed as the satisfiability of a second-order logical formula, asking…
In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…