Related papers: Properties of Eventually Positive Linear Input-Out…
A dynamical system is said to be reversible if, given an output, the input can always be recovered in a well-posed manner. Nevertheless, we argue that reversible systems that have a time-reversal symmetry, such as the Nonlinear…
This article examines the properties of positive solutions to fully nonlinear systems of integral equations involving Hardy and Wolff potentials. The first part of the paper establishes an optimal existence result and a Liouville type…
This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…
It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to…
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 propose a composite Lyapunov framework for nonlinear autonomous systems that ensures strict decay through a pair of differential inequalities. The approach yields integral estimates, quantitative convergence rates, vanishing of…
Starting from a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations is a Lyapunov function, establishing stability for two kinds of nonlinear…
A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…
Nonnegative probabilities that obey the sum rules may be assigned to a much wider family of sets of histories than decohering histories. The resulting {\it linearly positive histories} avoid the highly restrictive decoherence conditions and…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
We develop a method to control discrete-time systems with constant but initially unknown parameters from linear temporal logic (LTL) specifications. We introduce the notions of (non-deterministic) parametric and adaptive transition systems…
For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Differentially positive systems are systems whose linearization along trajectories is positive. Under mild assumptions, their solutions asymptotically converge to a one-dimensional attractor, which must be a limit cycle in the absence of…
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…
A direct data-driven iterative algorithm is developed to accurately estimate the $H_\infty$ norm of a linear time-invariant system from continuous operation, i.e., without resetting the system. The main technical step involves a…
Many recent data-driven control approaches for linear time-invariant systems are based on finite-horizon prediction of output trajectories using input-output data matrices. When applied recursively, this predictor forms a dynamic system…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time, but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov…
Lyapunov functions play a vital role in the context of control theory for nonlinear dynamical systems. Besides its classical use for stability analysis, Lyapunov functions also arise in iterative schemes for computing optimal feedback laws…