Related papers: Internally Hankel $k$-positive systems
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
A $k$-positive matrix is a matrix where all minors of order $k$ or less are positive. Computing all such minors to test for $k$-positivity is inefficient, as there are $\sum_{\ell=1}^k \binom{n}{\ell}^2$ of them in an $n\times n$ matrix.…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
Computing the viability kernel is key in providing guarantees of safety and proving existence of safety-preserving controllers for constrained dynamical systems. Current numerical techniques that approximate this construct suffer from a…
A Hopf manifold is a compact complex manifold of which the universal covering is C^n\{0}. In this note we show that any Hopf manifold admits a locally conformally Kaehler structure (shortly lcK structure), by constructing a complex analytic…
The reduced dynamics of an open quantum system $S$, interacting with its environment $E$, is not completely positive, in general. In this paper, we demonstrate that if the two following conditions are satisfied, simultaneously, then the…
In this paper, a class of indecomposable positive finite rank elementary operators of order $(n,n)$ are constructed. This allows us to give a simple necessary and sufficient criterion for separability of pure states in bipartite systems of…
A polarized variety is K-stable if, for any test configuration, the Donaldson-Futaki invariant is positive. In this paper, inspired by classical geometric invariant theory, we describe the space of test configurations as a limit of a direct…
We discuss connections between sequential system identification and control for linear time-invariant systems, often termed indirect data-driven control, as well as a contemporary direct data-driven control approach seeking an optimal…
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…
In this paper, we investigate the probabilistic formal verification of stochastic dynamical systems over continuous state spaces. Motivated by problems in state estimation and information-flow security, we introduce the notion of…
Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…
In this paper, we provide a system theoretic treatment of a new class of multilinear time-invariant (MLTI) systems in which the states, inputs and outputs are tensors, and the system evolution is governed by multilinear operators. The MLTI…
In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This framework can be used to represent e.g. a lumped mass fixed to a…
In the Reflection Positivity theory and its application to statistical mechanical systems, certain matrix inequalities play a central role. The Dyson-Lieb-Simon and Kennedy-Lieb-Shastry-Schupp inequalities constitute prominent examples. In…
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive-definite…
We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy…
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
We introduce $t$-Hermitian forms of arbitrary degree $k$, a natural extension of classical degree $k$ Hermitian forms obtained through a synthesis of the tensor transformation law and the $t$-product of third-order tensors. We show that…
We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori,…