Related papers: Positive Invariance Condition for Continuous Dynam…
Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…
We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
This note considers the maximal positively invariant set for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic set. The note utilizes a relatively direct, but apparently overlooked, fact stating…
Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an…
This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positive invariant set is…
We define some pointwise properties of topological dynamical systems and give pointwise conditions for such a system possesses positive topological entropy. We give sufficient conditions to obtain positive topological entropy for maps which…
In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…
We introduce notions of vector field and its (discrete time) flow on a chain complex. The resulting dynamical systems theory provides a set of tools with a broad range of applicability that allow, among others, to replace in a canonical way…
The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…
We establish a dynamical version of Kuratowski-Mycielski Theorem on the existence of "large" invariant dependent sets. We apply this result to the study of invariant chaotic sets in topological dynamical systems, simplify many known results…
Stability analysis of discrete-time switched systems under minimum dwell-time is studied using a new type of LMI conditions. These conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
In many scenarios, it is natural to model a plant's dynamical behavior using a hybrid dynamical system influenced by exogenous continuous-time inputs. While solution concepts and analytical tools for existence and completeness are well…
Low sampling frequency challenges the exact identification of the continuous-time (CT) dynamical system from sampled data, even when its model is identifiable. The necessary and sufficient condition is proposed -- which is built from…
We prove a vector-valued almost sure invariance principle for some classes of time dependent non-uniformly distance expanding dynamical systems. The models we have in mind are certain sequential versions of the smooth non-uniformly distance…
A sufficient condition for the stability of a system resulting from the interconnection of dynamical systems is given by the small gain theorem. Roughly speaking, to apply this theorem, it is required that the gains composition is…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
Under a mild technical assumption, we prove a necessary and sufficient condition for a totally real compacdt set in $\mathbb{C}^n$ to be rationally convex. This generalizes a classical result of Duval-Sibony
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…