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We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector…
We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers for nonlinear dynamical systems. The learning framework uses a demonstrator that implements a black-box, untrusted…
We extend the Lyapunov function technique, a fundamental tool for investigating asymptotic stability and existence of attractors for ordinary differential equations, by introducing the notion of a {\it strong Lyapunov function} for an…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…
This paper considers the problem of characterizing the stability region of a large-scale networked system comprised of dissipative nonlinear subsystems, in a distributed and computationally tractable way. One standard approach to estimate…
We consider polynomial differential equations and make a number of contributions to the questions of (i) complexity of deciding stability, (ii) existence of polynomial Lyapunov functions, and (iii) existence of sum of squares (sos) Lyapunov…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…
With the objective of developing computational methods for stability analysis of switched systems, we consider the problem of finding the minimal lower bounds on average dwell-time that guarantee global asymptotic stability of the origin.…
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
In this article, we provide a general strategy based on Lyapunov functionals to analyse global asymptotic stability of linear infinite-dimensional systems subject to nonlinear dampings under the assumption that the origin of the system is…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
In this paper we present an abstraction algorithm that produces a finite bisimulation quotient for an autonomous discrete-time linear system. We assume that the bisimulation quotient is required to preserve the observations over an…
The notion of Lyapunov function plays a key role in design and verification of dynamical systems, as well as hybrid and cyber-physical systems. In this paper, to analyze the asymptotic stability of a dynamical system, we generalize standard…