基于超优性原理的黏性解控制扩散的李雅普诺夫稳定性

LPV系统基于Lyapunov的稳定性、可镇定性与可检测性的不存在性证书

Certificates of Nonexistence for Lyapunov-Based Stability, Stabilizability and Detectability of LPV Systems

针对Lyapunov方法无法求解时结论不明确的问题，提出基于LMI的择一定理，通过计算“不存在性证书”证明LPV系统不存在多二次Lyapunov函数及其控制器和观测器。

后向结构随机系统的可控性与可镇定的Hautus型判据

Hautus-Type Criteria for Controllability and Stabilizability of Backward-Structured Stochastic Systems

针对后向结构随机线性系统，提出了精确可控性和可镇定性的随机Hautus型判据，核心发现是随机Hautus障碍是Lyapunov型算子的正半定特征矩阵，并建立了锥限制条件。

Asymptotic Stabilizability of Underactuated Hamiltonian Systems With Two Degrees of Freedom

For an underactuated (simple) Hamiltonian system with two degrees of freedom and one degree of underactuation, a rather general condition that ensures its stabilizability, by means of the existence of a (simple) Lyapunov function, was found in a recent paper by D.E. Chang within the context of the energy shaping method. Also, in the same paper, some additional assumptions were presented in order to ensure also asymptotic stabilizability. In this paper we extend these results by showing that above mentioned condition is not only sufficient, but also a necessary one. And, more importantly, we sh…

A Lie-bracket-based notion of stabilizing feedback in optimal control

For a control system two major issues can be considered: the stabilizability with respect to a given target, and the minimization of an integral functional (while the trajectories reach this target). Here we consider a problem where stabilizability or controllability are investigated together with the further aim of a "cost regulation", namely a state-dependent upper bounding of the functional. This paper is devoted to a crucial step in the program of establishing a chain of equivalences among degree-k stabilizability with regulated cost, asymptotic controllability with regulated cost, and the…

含源项系统的新李雅普诺夫函数

New Lyapunov functions for systems with source terms

本文将李雅普诺夫函数的指数权重扩展为双曲函数族，用于2×2平衡律系统，证明其能在更大参数范围内保证指数稳定性，并揭示大时延会显著缩小可镇定参数集，同时验证了双曲权重在拟线性双曲系统边界反馈稳定性分析中的有效性。

Stabilizability in optimal control

We extend the classical concepts of sampling and Euler solutions for control systems associated to discontinuous feedbacks by considering also the corresponding costs. In particular, we introduce the notions of Sample and Euler stabilizability to a closed target set (p0,W)-regulated cost, for some continuous, state-dependent function W and some positive constant p0: it roughly means that we require the existence of a stabilizing feedback K such that all the corresponding sampling and Euler solutions starting from a point z have suitably defined finite costs, bounded above by W(z)/p0. Then, we …

涉及李括号的 HJ 不等式与带成本调节的反馈可镇定性

HJ inequalities involving Lie brackets and feedback stabilizability with cost regulation

针对状态趋近闭目标集且支付非负代价的最优控制问题，将定义控制 Lyapunov 函数的经典耗散关系推广为涉及代价和迭代李括号的较弱微分不等式，提出度数 k 最小约束函数，并证明其存在性可构建基于李括号的反馈，在调节代价的同时实现系统采样镇定。

线性切换系统的切换信号反馈镇定

On feedback stabilization of linear switched systems via switching signal control

受最近在控制理论中的应用的启发，我们研究了切换系统的反馈可镇定性，其中允许选择切换信号作为$x(t)$的函数，以稳定系统。我们提出了新的算法，并分析了几个数学特性的问题，这是被忽视到现在为止，据我们所知。我们证明了复杂性的结果，（在）各种概念之间的等价性稳定，存在的李雅普诺夫函数，并提供了一个案例研究斯坦福大学和Urbano介绍的范例。

关于连续性和凸Lyapunov函数

On continuation and convex Lyapunov functions

该研究证明了在特定条件下，不同向量场之间可通过同伦保持原点稳定性，并探讨了其在稳定性证书和切换系统中的应用。

通过控制向量李雅普诺夫函数实现大规模系统的去中心化测量反馈稳定

Decentralized Measurement Feedback Stabilization of Large-scale Systems via Control Vector Lyapunov Functions

本文研究非线性互联系统的去中心化测量反馈稳定问题，提出输出控制向量李雅普诺夫函数概念，讨论了稳定条件，并通过例子展示方法。

基于李雅普诺夫函数约束的自适应动态规划

Adaptive dynamic programming using Lyapunov function constraints

本研究提出一种结合李雅普诺夫函数约束的自适应动态规划方法，采用无海森矩阵优化，可保证闭环稳定性，其评价网络方法在多初始条件下性能优于标称稳定控制器。

非线性扰动系统中的鲁棒控制Lyapunov值函数

Robust Control Lyapunov-Value Functions for Nonlinear Disturbed Systems

本文提出鲁棒控制Lyapunov值函数用于非线性扰动系统，通过哈密尔顿-雅可比可达性分析构建非光滑CLF，并解决维度灾难问题，通过预热启动和系统分解提升计算效率。