Related papers: Integral gains for non-autonomous Wazewski systems
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…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
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 investigate the feedback stability of multiple-input multiple-output linear time-invariant systems with combined gain and phase information. To begin with, we explore the stability condition for a class of so-called easily…
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…
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 paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of…
This paper introduces small-gain sufficient conditions for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound…
We consider the interconnections of arbitrary topology of a finite number of ISS hybrid systems and study whether the ISS property is maintained for the overall system. We show that if the small gain condition is satisfied, then the whole…
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,…
We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…
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…
We provide a detectability analysis for nonlinear large-scale distributed systems in the sense of exponential incremental input/output-to-state stability (i-IOSS). In particular, we prove that the overall system is exponentially i-IOSS if…
In recent years, attempts have been made to extend nonlinear small-gain theorems for input-to-state stability (ISS) from finite networks to countably infinite networks with finite indegrees. Under specific assumptions about the…
This paper examines impulsive controls related to nonautonomous impulsive integro-differential equations in Hilbert space, highlighting their significance. We establish the existence of the mild solution by using fixed point approach and…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
In a power grid with growing penetrations of renewable energy sources, inverters play a larger role in the dynamic interactions among network components. However, much is yet to be studied regarding inverter-dominated grid stability. This…
We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear…
We establish well-posedness results for non-autonomous semilinear input-output systems, the central assumption being the scattering-passivity of the considered semilinear system. We consider both systems with distributed control and…
We establish a number of new sufficient conditions for the existence of global (defined on the entire time axis) solutions of nonlinear nonautonomous systems by means of the Wazewski topological principle. The systems under consideration…