Related papers: A novel criterion for global incremental stability…
This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…
Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral input-to-state stability. We provide two proofs of this fact. One applies to general systems over Banach…
Dynamical systems, that are used to model power grids, the brain, and other physical systems, can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may…
In this paper, we'll show the robustness of global stability for perturbed dissipative dynamical systems.
For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform global asymptotic stability (UGAS), in which the decay rate and transient overshoot of solutions are requested to be…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
The present work provides two alternatives to formulate time-discounted incremental input/output-to-state stability (i-IOSS) as a suitable detectability notion for general nonlinear systems with non-additive disturbances. Both formulations…
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability…
This paper considers the equilibrium-free stability and performance analysis of discrete-time nonlinear systems. We consider two types of equilibrium-free notions. Namely, the universal shifted concept, which considers stability and…
Global stability of the systems has always been vital of importance; however, this concept has not yet been sufficiently developed for the nonlinear systems. This paper extends the Jacobian matrix so that this method be able to seek the…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
In the present work, sufficient conditions for global stabilization of nonlinear uncertain systems by means of discrete-delay static output feedback are presented. Illustrating examples show the efficiency of the proposed control strategy.
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as…
We present novel sufficient conditions for the global stability of equilibria in the case of nonlinear dynamics with analytic vector fields. These conditions provide stability criteria that are directly expressed in terms of the Taylor…