Stabilising compensators for linear time-varying differential systems

Oberst Ulrich

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Stabilising compensators for linear time-varying differential systems

机译：线性时变差分系统的稳定补偿器

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In this paper, we describe a constructive test to decide whether a given linear time-varying (LTV) differential system admits a stabilising compensator for the control tasks of tracking, disturbance rejection or model matching and construct and parametrise all of them if at least one exists. In analogy to the linear time-invariant (LTI) case, the ring of stable rational functions, noncommutative in the LTV situation, and the Kucera-Youla parametrisation play prominent parts in the theory. We transfer Blumthaler's thesis from the LTI to the LTV case and sharpen, complete and simplify the corresponding results in the book 'Linear Time-Varying Systems' by Bourles and Marinescu.

机译：在本文中，我们描述了一个建设性测试，以判定给定的线性时变（LTV）差分系统是否允许用于跟踪，干扰抑制或模型匹配的控制任务的稳定补偿器，并且如果至少有一个，则对它们进行构造和参数化存在。与线性时不变（LTI）情况类似，稳定有理函数的环在LTV情况下是不可交换的，并且Kucera-Youla参数化在理论中起着重要的作用。我们将Blumthaler的论文从LTI转移到LTV案例，并对Bourles和Marinescu的“线性时变系统”一书中的相应结果进行改进，完善和简化。

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《International Journal of Control》 |2016年第6期|共21页
作者
Oberst Ulrich;
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正文语种 eng
中图分类控制论、信息论（数学理论）;自动控制、自动控制系统;
关键词
93C05; 93B25; 93D20; 34H15; 93B52; 93D15; Behaviour; model matching; stabilising compensator; time-varying; disturbance rejection; tracking; exponential stability;

机译：93C05;93B25;93D20;34H15;93B52;93D15;性能;模型匹配;稳定补偿器;时变;干扰抑制;跟踪;指数稳定性;

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专利

1. Stabilising compensators for linear time-varying differential systems [J] . Oberst Ulrich International Journal of Control . 2016,第4a6期

机译：线性时变差分系统的稳定补偿器
2. Stabilisation of time-varying linear systems via Lyapunov differential equations [J] . Zhou B., Cai G.-B., Duan G.-R. International Journal of Control . 2013,第1a3期

机译：利用Lyapunov微分方程稳定时变线性系统。
3. An improved stability test and stabilisation of linear time-varying systems governed by second-order vector differential equations [J] . Shen-Lung Tung, Yau-Tarng Juang, Wei-Ying Wu, International journal of systems science . 2011,第10a12期

机译：基于二阶矢量微分方程的线性时变系统的改进稳定性测试和稳定性
4. Adaptive Practical Stabilisation Control for Nonlinear Uncertain Multi-agent Systems with Time-varying Parameters [C] . Huijin Fan, Wei Ma IEEE Information Technology, Networking, Electronic and Automation Control Conference . 2020

机译：非线性时变不确定多Agent系统的自适应实用稳定控制。
5. Output feedback tracking control of nonlinear time-varying systems by trajectory linearization. [D] . Huang, Rui. 2007

机译：轨迹线性化对非线性时变系统的输出反馈跟踪控制。
6. On the Approximated Reachability of a Class of Time-Varying Nonlinear Dynamic Systems Based on Their Linearized Behavior about the Equilibria: Applications to Epidemic Models [O] . Manuel De la Sen 2019

机译：基于对均衡的线性化行为的一类时变非线动力系统的近似可达性：应用于流行模型的应用
7. An extended-observer approach to robust stabilisation of linear differential-algebraic systems [O] . Alessandro Di Giorgio, Antonio Pietrabissa, Francesco Delli Priscoli, 2018

机译：直线差分代数系统强大稳定的扩展观察方法
8. Minimal Optimal Reduced-Order Compensators for Time-Varying Discrete-Time Systems [R] . van Willigenburg, L. G., de Koning, W. L. 1996

机译：时变离散时间系统的最小最优降阶补偿器

Stabilising compensators for linear time-varying differential systems

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