講座名稱：Guaranteed state estimation techniques where time is essential
講座人：Thach N. Dinh 副教授
讲座地點：騰訊會議直播（ID:456 443 821 https://meeting.tencent.com/dm/vmDiHy9kXK6K?rs=25）
Thach N. Dinh 2011年获得法国里昂研究所的自动化系统硕士学位。2014年获得巴黎萨克雷大学博士学位。2015年至2016年为日本九州工业大学博士后研究员。 2016 年至 2017年，他在法国高等技术大学担任助理教授。从 2017 年 9 月起为法国国立工艺学院的终身副教授。Thach N. Dinh主要研究领域为控制理论和应用、正系统、状态估计、区间观测器、输出反馈等。
In applied mathematics, using time may help to overcome obstacles. The most famous illustration of this remark is offered by systems which do not satisfy the celebrated Brockett's necessary stabilizability conditions, but nonetheless are asymptotically stabilizable by time-varying state feedbacks. There are other instances: we will review two distinct problems where using time cannot be avoided.
The Lecture 1 (1 hour) relies on the design of time-varying changes of coordinates, which transform a linear system into a nonnegative one. This design splits up into two steps. Firstly, we recall that any real matrix admits a real Jordan canonical form. Secondly, we transform systems in Jordan canonical form into positive systems. Consequently, it is shown that, for any time-invariant exponentially stable discrete time linear system with additive disturbances, time-varying exponentially stable discrete-time interval observers can be constructed.
The Lecture 2 (1 hour) proposes new design techniques of deadbeat observer and fixed-time interval estimator incorporating an artificial constant delay. The key idea relies on the use of past values of the input and the output of the studied system. No information on the bound of the initial conditions was needed in our development and we provide exact values of the solutions in the absence of disturbances and a lower and upper bounds when the disturbances are present after a fixed time which can be tuned.