Related papers: Reduction Theorems for Hybrid Dynamical Systems
In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory…
Oscillatory behavior is a key property of many biological systems. The Small-Gain Theorem (SGT) for input/output monotone systems provides a sufficient condition for global asymptotic stability of an equilibrium and hence its violation is a…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is…
In this work we examine the stability of some classes of integrals, and in particular with respect to homogenization. The prototypical case is the homogenization of quadratic energies with periodic coefficients perturbed by a term vanishing…
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 notion of an attractor has various definitions in the theory of dynamical systems. Under compactness assumptions, several of those definitions coincide and the theory is rather complete. However, without compactness, the picture becomes…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
This paper establishes a far-reaching connection between the Finite-Difference Time-Domain method (FDTD) and the theory of dissipative systems. The FDTD equations for a rectangular region are written as a dynamical system having the…
Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…
Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by…
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the subsystems are only almost globally asymptotically stable. The result is extended to upper triangular systems of arbitrary…
This paper deals with existence and robust stability of hybrid limit cycles for a class of hybrid systems given by the combination of continuous dynamics on a flow set and discrete dynamics on a jump set. For this purpose, the notion of…
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…
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,…
We show that a sub-homogeneous positive monotone system with bounded heterogeneous time-varying delays is globally asymptotically stable if and only if the corresponding delay-free system is globally asymptotically stable. The proof is…
In this note, we show how certain properties of Goldbeter's 1995 model for circadian oscillations can be proved mathematically, using techniques from the recently developed theory of monotone systems with inputs and outputs. The theory…