相关论文: A small-gain theorem for nonlinear stochastic syst…

This paper is a continuation of the paper \cite{JL}, which focuses on exploring the global stability of nonlinear stochastic feedback systems on the nonnegative orthant driven by multiplicative white noise and presenting a couple of…

In this paper, we study the existence of random periodic solutions for nonlinear stochastic differential equations with additive white noise. We extend the input-to-state characteristic operator of the system to the non-autonomous…

Convergent, contractive or incremental stability properties of nonlinear systems have attracted interest for control tasks such as observer design, output regulation and synchronization. The convergence property plays a central role in the…

We introduce the concept of non-uniform input-to-state stability for networks. It combines the uniform global stability with the uniform attractivity of any subnetwork, while it allows for non-uniform convergence of all components. For an…

We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provided that the gain operator satisfies a certain small-gain…

Motivated by a paradigm shift towards a hyper-connected world, we develop a computationally tractable small-gain theorem for a network of infinitely many systems, termed as infinite networks. The proposed small-gain theorem addresses…

This paper presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponentially input-to-state stable, we show that if the gain operator,…

A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to…

We prove a small-gain theorem for interconnections of $n$ nonlinear heterogeneous input-to-state stable (ISS) control systems of a general nature, covering partial, delay and ordinary differential equations. Furthermore, for the same class…

This paper extends the nonlinear ISS small-gain theorem to a large-scale time delay system composed of three or more subsystems. En route to proving this small-gain theorem for systems of differential equations with delays, a small-gain…

A Small-Gain Theorem, which can be applied to a wide class of systems that includes systems satisfying the weak semigroup property, is presented in the present work. The result generalizes all existing results in the literature and exploits…

A new Small-Gain Theorem is presented for general nonlinear control systems. The novelty of this research work is that vector Lyapunov functions and functionals are utilized to derive various input-to-output stability and input-to-state…

Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state…

Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…

This paper presents a unification and a generalization of the small-gain theory subsuming a wide range of existing small-gain theorems. In particular, we introduce small-gain conditions that are necessary and sufficient to ensure…

This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.

We provide a new global small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a recent small-gain theorem of Angeli and Sontag for monotone systems with…

This paper provides a Lyapunov-based small-gain theorem for input-to-state stability (ISS) of networks composed of infinitely many finite-dimensional systems. We model these networks on infinite-dimensional $\ell_{\infty}$-type spaces. A…

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to…

We study the input-to-state stability (ISS) of boundary control systems allowing for infinitely many boundary couplings. Using semigroup perturbation theory and the theory of positive linear operators on Banach lattices, we derive a…