In this paper, we prepare the analysis of differential-algebraic equations (DAEs) with regard to properties as positivity, stability or contractivity. To study these properties, the differential and algebraic components of a DAE must be separated to quantify when they exhibit the desired property. For the differential components, the common results for ordinary differential equations (ODEs) can...

We present a novel way to compare the statistical cost of privacy mechanisms using their Dobrushin coefficient. Specifically, we provide upper and lower bounds for the Dobrushin coefficient of a privacy mechanism in terms of its maximal leakage and local differential privacy guarantees. Given the geometric nature of the Dobrushin coefficient, this approach provides some insights into the genera...

In this paper we study the stability and L2-gain properties of a class of hybrid systems that exhibit linear flow dynamics, periodic time-triggered jumps and arbitrary nonlinear jump maps. This class of hybrid systems is relevant for a broad range of applications including periodic event-triggered control, sampled-data reset control, sampled-data saturated control, and certain networked control...

We study in this paper nonlinear subdivision schemes in a multivariate setting allowing arbitrary dilation matrix. We investigate the convergence of such iterative process to some limit function. Our analysis is based on some conditions on the contractivity of the associated scheme for the differences. In particular, we show the regularity of the limit function, in L and Sobolev spaces.

The convergence of fractal operator F used in image compression is investigated by analysis of block innuence graph and pixel innuence graph. The graph stability condition in block innuence graph implies eventual contractivity condition which is suucient for the operator iteration convergence. The graph stability condition in pixel innuence graph appears to be suucient and necessary for converg...

This paper investigates stability conditions of continuous-time Hopfield and firing-rate neural networks by leveraging contraction theory. First, we present a number useful general algebraic results on matrix polytopes products symmetric matrices. Then, give sufficient for strong weak Euclidean contractivity, i.e., contractivity with respect to the ℓ2 norm, both models weights (possibly) non-sm...

This paper presents several results on consistency properties of simulation-based estimators for a general class of continuous dynamic models. The consistency of these estimators follows from a uniform convergence property of the sample paths over the vector of parameters. This convergence property is established under certain contractivity and monotonicity conditions on the dynamics of the sys...