Related papers: A data-independent distance to infeasibility for l…
This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
We study inhomogeneous semilinear parabolic equations with source term f independent of time u_{t}={\Delta}u+u^{p}+f(x) on a metric measure space, subject to the conditions that f(x)\geq 0 and u(0,x)=\phi(x)\geq 0. By establishing…
This paper explores the observability and estimation capability of dynamical systems using predominantly relative measurements of the system's state-space variables, with minimal to no reliance on absolute measurements of these variables.…
Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
We analyze the probability that a random m-dimensional linear subspace of R^n both intersects a regular closed convex cone C\subseteq R^n and lies within distance \alpha of an m-dimensional subspace not intersecting C (except at the…
For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…
Determining the distance between a controllable system to the set of uncontrollable systems, namely, the controllability radius problem, has been extensively studied in the past. However, the opposite direction, that is, determining the…
This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of…
A physical measure on the attractor of a system describes the statistical behavior of typical orbits. An example occurs in unimodal dynamics. Namely, all infinitely renormalizable unimodal maps have a physical measure. For Lorenz dynamics,…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
In this article we study the structured distance to singularity for a nonsingular matrix $A\in\mathbb{C}^{n\times n}$, with a prescribed linear structure $\mathcal{S}$ (for instance, a sparsity pattern, or a real Toeplitz structure), i.e.,…
This article deals with the problem of testing conditional independence between two random vectors ${\bf X}$ and ${\bf Y}$ given a confounding random vector ${\bf Z}$. Several authors have considered this problem for multivariate data.…
Determining the reachable set for a given nonlinear system is critically important for autonomous trajectory planning for reach-avoid applications and safety critical scenarios. Providing the reachable set is generally impossible when the…
The paper develops a novel and general methodology to characterize the nonlinearity of structural systems and to provide a mathematically proven basis for applying partial safety factors to nonlinear structural systems. It establishes, for…
We deal with nonlinear systems of parabolic type satisfying component-wise structural conditions. The nonlinear terms are Carath\'eodory maps having controlled growth with respect to the solution and the gradient and the data are in…
We propose to derive deviation measures through the Minkowski gauge of a given set of acceptable positions. We show that, given a suitable acceptance set, any positive homogeneous deviation measure can be accommodated in our framework. In…
We describe and analyze an interior-point method to decide feasibility problems of second-order conic systems. A main feature of our algorithm is that arithmetic operations are performed with finite precision. Bounds for both the number of…
This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified…