相关论文: Hybrid Systems as Coalgebras: Lyapunov Morphisms f…
Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic…
Lyapunov's theorem provides a foundational characterization of stable equilibrium points in dynamical systems. In this paper, we develop a framework for stability for F-coalgebras. We give two definitions for a categorical setting in which…
This paper studies finite-time stability of a class of hybrid systems. We present sufficient conditions in terms of multiple generalized Lyapunov functions for the origin of the hybrid system to be finite-time stable. More specifically, we…
Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions,…
The paper proposes a framework for the construction of solutions to a hybrid dynamical system that exhibit Zeno behavior. A new approach that enables solution to be prolonged after reaching its Zeno time is developed. It allows for a…
We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…
Hybrid systems exhibit phenomena which do not occur in systems with continuous vector fields. One such phenomenon - Zeno executions - is characterized by an infinite number of discrete events or transitions occurring over a finite interval…
This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common…
This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov-Razumikhin functions and Lyapunov-Krasovskii functionals, Lyapunov-based sufficient…
Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for…
We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper provides a systematic exposition of Lyapunov stability for compact sets in locally compact metric spaces. We explore foundational concepts, including neighborhoods of compact sets, invariant sets, and the properties of dynamical…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
Hybrid dynamical systems have proven to be a powerful modeling abstraction, yet fundamental questions regarding the dynamical properties of these systems remain. In this paper, we develop a novel class of relaxations which we use to recover…
Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those…
We introduce a notion of stability for equilibrium measures in holomorphic families of endomorphisms of CP(k) and prove that it is equivalent to the stability of repelling cycles and equivalent to the existence of some measurable…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as…
We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global…