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Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…
Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…
In statistical process control, procedures are applied that require relatively strict conditions for their use. If such assumptions are violated, these methods become inefficient, leading to increased incidence of false signals. Therefore,…
Deep Networks have been shown to provide state-of-the-art performance in many machine learning challenges. Unfortunately, they are susceptible to various types of noise, including adversarial attacks and corrupted inputs. In this work we…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
The system property of ``having integer coefficients,'' that is, a transfer function has an integer monic polynomial as its denominator, is significant in the field of encrypted control as it is required for a dynamic controller to be…
The stabilizability of wireless networked control systems (WNCSs) is a deterministic binary valued parameter proven to hold if the communication data rate is higher than the sum of the logarithm of unstable eigenvalues of the open-loop…
Influence diagram is a graphical representation of belief networks with uncertainty. This article studies the structural properties of a probabilistic model in an influence diagram. In particular, structural controllability theorems and…
A goal of this work is to study the dynamics in the complement of KAM tori with focus on non-local robust transitivity. We introduce $C^r$ open sets ($r=1, 2, ..., \infty$) of symplectic diffeomorphisms and Hamiltonian systems, exhibiting…
We discuss the problem of robust representations of stable and passive transfer functions in particular coordinate systems, and focus in particular on the so-called port-Hamiltonian representations. Such representations are typically far…
A nonlinear control system is said to be weakly contractive in the control if the flow that it generates is non-expanding (in the sense that the distance between two trajectories is a non-increasing function of time) for some fixed…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…
In this paper, we propose a perturbation framework to measure the robustness of graph properties. Although there are already perturbation methods proposed to tackle this problem, they are limited by the fact that the strength of the…
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…
We consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function) under the two metrics are the same, then the two metrics are…
We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…