Lower bounds and dense discontinuity phenomena for the stabilizability radius of linear switched systems

On Switching Stabilizability for Continuous-Time Switched Linear Systems

This paper studies switching stabilization problems for continuous-time switched linear systems. We consider four types of switching stabilizability defined under different assumptions on the switching control input. The most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time-varying system is asymptotically stable. Discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length. In addition, we define feedback stabilizability in Filippov …

含奇异矩阵的线性切换系统的可镇定性与下谱半径

Stabilizability and lower spectral radius for linear switched systems with singular matrices

研究含奇异矩阵的线性离散时间切换系统的可镇定性问题，提出适用于任意矩阵集的可镇定半径新下界，并建立其与联合谱子半径的关系，特别分析了一类由奇异矩阵和旋转矩阵组成的二维切换系统的可镇定半径及参数集的Hausdorff维数。

离散时间切换线性系统固定时间及任意快速指数稳定化

Fixed-Time and Arbitrarily Fast Exponential Stabilization of Discrete-Time Switched Linear Systems

本文研究了离散时间切换线性控制系统的固定时间稳定性，通过几何方法推导出在指定步数内稳定条件，提出模式依赖和模式无关两种控制方法，并通过结构分解简化分析与设计，证明固定时间和任意快速指数稳定等价性。

On feedback stabilization of linear switched systems via switching signal control

Motivated by recent applications in control theory, we study the feedback stabilizability of switched systems, where one is allowed to chose the switching signal as a function of $x(t)$ in order to stabilize the system. We propose new algorithms and analyze several mathematical features of the problem which were unnoticed up to now, to our knowledge. We prove complexity results, (in-)equivalence between various notions of stabilizability, existence of Lyapunov functions, and provide a case study for a paradigmatic example introduced by Stanford and Urbano.

Decay rates for stabilization of linear continuous-time systems with random switching

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time. This result is related to the stabilizability problem for linear persistently excited systems.

切换与受约束线性系统的数据驱动镇定

Data-driven stabilization of switched and constrained linear systems

本文针对未知切换线性系统，基于Lyapunov-Metzler不等式提出数据驱动双线性规划方法，直接设计可镇定控制器并保证H2/H∞性能，同时通过松弛方法降低计算成本，无需各模态可镇定性。