Related papers: A Small-Gain Theorem with Applications to Input/Ou…
This paper is devoted to two issues. One is to provide Lyapunov-based tools to establish integral input-to-state stability (iISS) and input-to-state stability (ISS) for some classes of nonlinear parabolic equations. The other is to provide…
This paper presents a fundamental relation between Output Asymptotic Gains (OAG) and Input-to-Output Stability (IOS) gains for linear systems. For any Input-to-State Stable, strictly causal linear system the minimum OAG is equal to the…
In this paper, the incremental stability of interconnected switched nonlinear systems is discussed. The nature of switching considered is state-dependent. The incremental stability of the switched interconnected system is a stronger…
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.
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…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
This paper studies a small-gain theorem for nonlinear stochastic equations driven by additive white noise in both trajectories and stationary distribution. Motivated by the most recent work of Marcondes de Freitas and Sontag \cite{FS3}, we…
We prove that under a small-gain condition, an interconnection of two globally incrementally exponentially stable systems inherits this property on any compact connected forward invariant set. It is also demonstrated that the…
Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient…
This work provides an example that motivates and illustrates theoretical results related to a combination of small-gain and density propagation conditions. Namely, in case the small-gain fails to hold at certain points or intervals the…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a…
A notion of detectability for nonlinear systems is discussed. Within the framework of ``input to state stability'' (ISS), a dual notion of ``output to state stability'' (OSS), and a more complete detectability notion, ``input-output to…
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…
In this paper, we develop a new approach to study gain operators built from the interconnection gains of infinite networks of dynamical systems. Our focus is on the construction of paths of strict decay which are used for building Lyapunov…
We present a new sufficient condition for finite-gain $L_2$ input-to-output stability of a networked system. The condition requires a matrix, that combines information on the $L_2$ gains of the sub-systems and their interconnections, to be…
Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the…
A notion of "asymptotic Cauchy gain" for input/output systems, and an associated small-gain principle, are introduced. A Lyapunov-like characterization allows the computation of these gains for state-space systems, and the formulation of…
New trajectory-based small-gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous…
This paper considers small gain theorems for the global asymptotic and exponential input-to-state stability for discrete time time-delay systems using Razumikhin-type Lyapunov function. Among other things, unlike the existing literature, it…