CHARACTERIZATIONS OF INTEGRAL INPUT-TO-STATE STABILITY FOR BILINEAR SYSTEMS IN INFINITE DIMENSIONS

Mironchenko Andrii; Ito Hiroshi

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CHARACTERIZATIONS OF INTEGRAL INPUT-TO-STATE STABILITY FOR BILINEAR SYSTEMS IN INFINITE DIMENSIONS

机译：无限维双线性系统积分输入至状态稳定性的刻画

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摘要

For bilinear infinite-dimensional dynamical systems, we show the equivalence between uniform global asymptotic stability and integral input-to-state stability. We provide two proofs of this fact. One applies to general systems over Banach spaces. The other is restricted to Hilbert spaces, but is more constructive and results in an explicit form of iISS Lyapunov functions.

机译：对于双线性无穷维动力系统，我们证明了一致的全局渐近稳定性和积分的输入至状态稳定性之间的等价性。我们提供了两个事实证明。一种适用于Banach空间上的一般系统。另一个仅限于希尔伯特空间，但更具建设性，并形成了iISS Lyapunov函数的显式形式。

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《Mathematical control and related fields》 |2016年第3期|共20页
作者
Mironchenko Andrii; Ito Hiroshi;
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正文语种 eng
中图分类数学;
关键词
Bilinear systems; infinite-dimensional systems; integral input-to-state stability; Lyapunov methods;

机译：双线性系统;无穷维系统;输入到状态的整体稳定性;Lyapunov方法;

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专利

1. CHARACTERIZATIONS OF INTEGRAL INPUT-TO-STATE STABILITY FOR BILINEAR SYSTEMS IN INFINITE DIMENSIONS [J] . Mironchenko Andrii, Ito Hiroshi Mathematical control and related fields . 2016,第3期

机译：无限维双线性系统积分输入至状态稳定性的刻画
2. Lyapunov functions for input-to-state stability of infinite-dimensional systems with integrable inputs [J] . Andrii Mironchenko IFAC PapersOnLine . 2020,第2期

机译：Lyapunov采用可集成输入的无限维系统的输入到状态稳定性
3. Input-to-State Stability of Infinite-Dimensional Systems: Recent Results and Open Questions [J] . Mironchenko Andrii, Prieur Christophe SIAM Review . 2020,第3期

机译：无限维系统的输入到状态稳定性：最近的结果和开放性问题
4. Integral input-to-state stability of bilinear infinite-dimensional systems [C] . Mironchenko Andrii, Ito Hiroshi IEEE Annual Conference on Decision and Control . 2014

机译：双线性无穷维系统的输入到状态积分稳定性
5. Control of infinite dimensional bilinear systems: Applications to quantum control systems. [D] . Zhang, Qin. 2009

机译：无限维双线性系统的控制：在量子控制系统中的应用。
6. An input-to-state stability approach to verify almost global stability of a synchronous-machine-infinite-bus system [O] . Johannes Schiffer, Denis Efimov, Romeo Ortega, -1

机译：一种输入到状态稳定性方法用于验证同步机器无限总线系统的几乎全局稳定性
7. Characterizations of integral input-to-state stability for bilinear systems in infinite dimensions [O] . Mironchenko, Andrii, Ito, Hiroshi 2016

机译：双线性积分输入到状态稳定性的刻画无限维度的系统
8. Linear and Bilinear Infinite-Dimensional Representations of Finite-Dimensional Nonlinear Systems [R] . Banks, S. P., Ashtiani, A. 1984

机译：有限维非线性系统的线性和双线性无限维表示

CHARACTERIZATIONS OF INTEGRAL INPUT-TO-STATE STABILITY FOR BILINEAR SYSTEMS IN INFINITE DIMENSIONS

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