Nguyen, Nguyen Trung (2024) Positive Linear Systems. Bachelor's Thesis, Applied Mathematics.
|
Text
bAppM2024NguyenNT.pdf Download (520kB) | Preview |
|
![[img]](https://fse.studenttheses.ub.rug.nl/style/images/fileicons/text.png) |
Text
toestemming_ Nguyen Trung Nguyen _ degree programme_ Applied Mathematics.pdf Restricted to Registered users only Download (134kB) |
Abstract
This thesis serves as an introduction to "Positive Systems Theory" by providing an overview of the fundamental results concerning positive systems. Generally speaking, a dynamical system is positive if its describing variables only take nonnegative values. Motivated by various real-life examples, we study linear time-invariant systems in continuous and in discrete time and we provide characterisations for their positivity. Next, we show several ways to verify whether a positive system is asymptotically stable, which reveal that checking stability properties of large-scale systems remains practically feasible. We proceed with the widely recognised Kalman-Yakubovich-Popov lemma adapted to positive systems, which bridges the frequency domain and state space. Then, we tackle the positive stabilisation problem, i.e. we seek to design a controller, which achieves both stability and positivity. Finally, we take first steps towards data-driven analysis and control of positive systems by solving the problem of system identification. Throughout this thesis, we demonstrate our results with numerical examples.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Waarde, H.J. van and Camlibel, M.K. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 17 Jul 2024 07:46 |
| Last Modified: | 17 Jul 2024 07:46 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/33477 |
Actions (login required)
 |
View Item |