相关论文: Further Results on Lyapunov Functions for Slowly T…

This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…

This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means.…

Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing…

While there has been increasing interest in using neural networks to compute Lyapunov functions, verifying that these functions satisfy the Lyapunov conditions and certifying stability regions remain challenging due to the curse of…

Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…

First-order methods are often analyzed via their continuous-time models, where their worst-case convergence properties are usually approached via Lyapunov functions. In this work, we provide a systematic and principled approach to find and…

This work has the goal of briefly surveying some key stabilization techniques for general nonlinear systems, for which, as it is well known, a smooth control Lyapunov function may fail to exist. A general overview of the situation with…

This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is…

We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…

The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…

Performance analysis for linear time-invariant (LTI) systems has been closely tied to quadratic Lyapunov functions ever since it was shown that LTI system stability is equivalent to the existence of such a Lyapunov function. Some metrics…

In this paper, we study the stability problem of a stochastic, nonlinear, discrete-time system. We introduce a linear transfer operator-based Lyapunov measure as a new tool for stability verification of stochastic systems. Weaker…

This paper proposes several Converse Lyapunov Theorems for nonlinear dynamical systems defined on smooth connected Riemannian manifolds and characterizes properties of corresponding Lyapunov functions in a normal neighborhood of an…

This paper considers a wide class of smooth continuous dynamic nonlinear systems (control objects) with a measurable vector of state. The problem is to find a special function (Lyapunov function), which in the framework of the second…

This work studies the problem of searching for homogeneous polynomial Lyapunov functions for stable switched linear systems. Specifically, we show an equivalence between polynomial Lyapunov functions for systems of this class and quadratic…

It is an interesting open problem to achieve adaptive prescribed-time control for strict-feedback systems with unknown and fast or even abrupt time-varying parameters. In this paper we present a solution with the aid of several design and…

We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions…

The robust tracking and model following problem of linear discrete-time systems is investigated in this paper. An approach to design robust tracking controllers is proposed. The system is controlled to track dynamic inputs generated from a…

We consider an abstract class of infinite-dimensional dynamical systems with inputs. For this class, the significance of noncoercive Lyapunov functions is analyzed. It is shown that the existence of such Lyapunov functions implies…

Starting from a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations is a Lyapunov function, establishing stability for two kinds of nonlinear…