Related papers: On differential passivity of physical systems

The dynamics of units (molecules) with slowly relaxing internal states is studied as an iterated function system (IFS) for the situation common in e.g. biological systems where these units are subjected to frequent collisional interactions.…

We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their…

Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. A…

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…

For linear control systems, the usual state feedback stabilizability has two components: one is a continuous observation mode (i.e., to observe solutions continuously in time), and the other is a class of feedback laws (which is usually the…

In this paper, we investigate a class of port-Hamiltonian systems with singular vector fields. We show that, under suitable conditions, their interconnection with passive systems ensures convergence to a prescribed non-equilibrium steady…

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to…

In this paper, we develop spectral analysis of a discrete non-Hermitian quantum system that is a discrete counterpart of some continuous quantum systems on a complex contour. In particular, simple conditions for discreteness of the spectrum…

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

Differential Privacy (DP) is an important privacy-enhancing technology for private machine learning systems. It allows to measure and bound the risk associated with an individual participation in a computation. However, it was recently…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

While port-Hamiltonian descriptor systems are known to be stable and passive, they may not be asymptotically stable or strictly passive. Necessary and sufficient conditions are presented when these properties as well as the regularity and…

This paper investigates an energy conservation and dissipation -- passivity -- aspect of dynamic models in evolutionary game theory. We define a notion of passivity using the state-space representation of the models, and we devise…

We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…

In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…

We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson…

We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…

In this work we systematically analyze general properties of differential equations used as machine learning models. We demonstrate that the gradient of the loss function with respect to to the hidden state can be considered as a…