Related papers: Positive Invariance Condition for Continuous Dynam…
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…
This paper proposes a Nagumo-type invariance condition for differential inclusions defined on closed constraint sets. More specifically, given a closed set to render forward invariant, the proposed condition restricts the system's dynamics,…
This paper focuses on a class of additive perturbations in dynamical systems. An equivalence statement for this construction is discovered, and consequently, a method of checking a notion of positive invariance with perturbation. The…
In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear…
The integrability has been playing an essential role in the field of differential equations. This property may better help us obtain the topological structure and even the global dynamics for the considered system. A system is called…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
We consider systems of linear partial differential equations, which contain only second and first derivatives in the $x$ variables and which are uniformly parabolic in the sense of Petrovski\v{\i} in the layer ${\mathbb R}^n\times [0,T]$.…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
A method of proving local continuity of concave functions on convex set possessing the $\mu$-compactness property is presented. This method is based on a special approximation of these functions. The class of $\mu$-compact sets can be…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies obtained for linear systems without zero order term in bounded domains and…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA)…
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a…
In this paper we study a criterion for the viability of stochastic semilinear control systems on a real, separable Hilbert space. The necessary and sufficient conditions are given using the notion of stochastic quasi-tangency. As a…
A new class of projected dynamical systems of third order is investigated for quasi (parametric) variational inequalities in which the convex set in the classical variational inequality also depends upon the solution explicitly or…