Related papers: Ordering and refining path-complete Lyapunov funct…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
In this work, the issue of estimation of reachable sets in continuous bimodal piecewise affine systems is studied. A new method is proposed, in the framework of ellipsoidal bounding, using piecewise quadratic Lyapunov functions. Although…
In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems…
We initiate a formal study on the use of low-dimensional latent representations of dynamical systems for verifiable control synthesis. Our main goal is to enable the application of verification techniques -- such as Lyapunov or barrier…
We use Lyapunov type functions to give new conditions under which a homeomorphism of a compact metric space has the shadowing property. These conditions are applied to establish the topological stability of some homeomorphisms with…
This article presents a novel numerically tractable technique for synthesizing Lyapunov functions for equilibria of nonlinear vector fields. In broad strokes, corresponding to an isolated equilibrium point of a given vector field, a…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by…
Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often…
Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…
Computer assisted procedures of Lyapunov functions defined in given neighborhoods of fixed points for flows and maps are discussed. We provide a systematic methodology for constructing explicit ranges where quadratic Lyapunov functions…
In the article$^a$, the authors introduced a time-varying Lyapunov function for the stability analysis of nonlinear systems whose motion is governed by standard Newton-Euler equations. The authors established asymptotic stability with the…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
While ensuring stability for linear systems is well understood, it remains a major challenge for nonlinear systems. A general approach in such cases is to compute a combination of a Lyapunov function and an associated control policy.…
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…
We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…
Stability analysis of switched systems, characterized by multiple operational modes and switching signals, is challenging due to their nonlinear dynamics. While frameworks such as multiple Lyapunov functions (MLF) provide a foundation for…
We present a new data-driven method to provide probabilistic stability guarantees for black-box switched linear systems. By sampling a finite number of observations of trajectories, we construct approximate Lyapunov functions and deduce the…
We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a…
Safety is essential for autonomous systems, in particular for interconnected systems in which the interactions among subsystems are involved. Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we…