Related papers: A Lyapunov-based small-gain theorem for infinite n…
In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to…
We consider piecewise linear discrete time macroeconomic models, which possess a continuum of equilibrium states. These systems are obtained by replacing rational inflation expectations with a boundedly rational, and genuinely sticky,…
Minimal input/output selection is investigated in this paper for each subsystem of a networked system. Some novel sufficient conditions are derived respectively for the controllability and observability of a networked system, as well as…
While training error of most deep neural networks degrades as the depth of the network increases, residual networks appear to be an exception. We show that the main reason for this is the Lyapunov stability of the gradient descent…
In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without…
Lately, data-driven control has become a widespread area of research. A few recent big-data based approaches for data-driven control of nonlinear systems try to use classical input-output techniques to design controllers for systems for…
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…
We compute how small input perturbations affect the output of deep neural networks, exploring an analogy between deep networks and dynamical systems, where the growth or decay of local perturbations is characterised by finite-time Lyapunov…
We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this work we extend this theory to a class of operators on Banach spaces…
We consider stability and network capacity in discrete time queueing systems. Relationships between four common notions of stability are described. Specifically, we consider rate stability, mean rate stability, steady state stability, and…
This paper is devoted to study stability of Lyapunov exponents and simplicity of Lyapunov spectrum for bounded random compact operators on a separable infinite-dimensional Hilbert space from a generic point of view generated by the…
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…
A new framework for adaptive regulation to invariant sets is proposed. Reaching the target dynamics (invariant set) is to be ensured by state feedback while adaptation to parametric uncertainties is provided by additional adaptation…
We show that a linear Young differential equation generates a topological two-parameter flow, thus the notions of Lyapunov exponents and Lyapunov spectrum are well-defined. The spectrum can be computed using the discretized flow and is…
The cyclic feedback interconnection of $n$ subsystems is the basic building block of control theory. Many robust stability tools have been developed for this interconnection. Two notable examples are the small gain theorem and the Secant…
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…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…