Related papers: Converse negative imaginary theorems
We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as…
It has been suggested that adversarial examples cause deep learning models to make incorrect predictions with high confidence. In this work, we take the opposite stance: an overly confident model is more likely to be vulnerable to…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
The best developed formulation of closed system quantum theory that handles multiple-time statements, is the consistent (or decoherent) histories approach. The most important weaknesses of the approach is that it gives rise to many…
This paper deals with strong versions of input-to-state stability and integral input-to-state stability of infinite-dimensional linear systems with an unbounded input operator. We show that infinite-time admissibility with respect to inputs…
Convolutional and recurrent neural networks have been widely employed to achieve state-of-the-art performance on classification tasks. However, it has also been noted that these networks can be manipulated adversarially with relative ease,…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Based on the invariance principle of differential equations a simple, systematic, and rigorous feedback scheme with the variable feedback strength is proposed to stabilize nonlinearly any chaotic systems without any prior analytical…
Robustness is established for the predictor feedback for linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. Prior results have addressed qualitatively…
We study the well-posedness and stability of an impedance passive infinite-dimensional linear system under nonlinear feedback of the form $u(t)=\phi(v(t)-y(t))$, where $\phi$ is a monotone function. Our first main result introduces…
This paper analyzes internal stability of a discrete-time feedback system with a ReLU nonlinearity. This feedback system is motivated by recurrent neural networks. We first review existing static quadratic constraints (QCs) for…
Negative feedback is a powerful approach capable of improving several aspects of a system. In linear electronics, it has been critical for allowing invariance to device properties. Negative feedback is also known to enhance linearity in…
Counterfactual explanations describe how to modify a feature vector in order to flip the outcome of a trained classifier. Obtaining robust counterfactual explanations is essential to provide valid algorithmic recourse and meaningful…
This note studies the robust output feedback stabilization problem of multi-input multi-output invertible nonlinear systems with output-dependent multipliers. An "ideal" state feedback is first designed under certain mild assumptions. Then,…
This paper studies the feedback stabilization of abstract Cauchy problems with unbounded output operators by finite-dimensional controllers. Both necessary conditions and sufficient conditions for feedback stabilizability are presented. The…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
This paper analyzes the robust feedback stability of a single-input-single-output stable linear time-invariant (LTI) system against four different classes of nonlinear systems using the Zames-Falb multipliers. The contribution is fourfold.…
We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several…
In this paper, a method is presented to synthesize neural network controllers such that the feedback system of plant and controller is dissipative, certifying performance requirements such as L2 gain bounds. The class of plants considered…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…