Yin, Feiyuan (2026) Error Bounds and Efficiency of Time-Limited Balanced Truncation. Research Project, System and Control.
|
Text
SystemsandControl2026YinF.pdf Download (892kB) | Preview |
Abstract
Balanced truncation is a widely used model reduction method because it preserves stability and provides computable error bounds for stable linear systems. However, its standard error analysis assumes zero initial conditions, which is not appropriate for switched linear systems, where each intermediate mode typically starts from a state inherited from the previous one. This thesis investigates the finite-horizon balanced truncation in this setting, with particular focus on midpoint-based balanced truncation (MPBT). First, a full-interval L_2 error bound is derived for systems with nonzero initial conditions by introducing history- and future-dependent Gramians. Although such a bound can be established, the analysis shows that its reliance on Gronwall's inequality leads to overly conservative estimates for short mode durations. Second, it is shown that the same continuous-time bounding framework cannot be extended directly to MPBT, since its interval-wise midpoint projections introduce mismatches at switching boundaries and invalidate the standard output-based bounding argument. Finally, the numerical examples compare MPBT with full-interval and global reduction methods. The results indicate that MPBT improves approximation accuracy when dominant state directions vary significantly across modes, but becomes less effective when the system dynamics are more uniformly distributed.
| Item Type: | Thesis (Research Project) |
|---|---|
| Supervisor name: | Trenn, S. and Besselink, B. |
| Degree programme: | System and Control |
| Thesis type: | Research Project |
| Language: | English |
| Date Deposited: | 14 Apr 2026 12:01 |
| Last Modified: | 14 Apr 2026 12:01 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37291 |
Actions (login required)
 |
View Item |