Abstract
From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 982-1006 |
| Number of pages | 25 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 29 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2007 |
| Externally published | Yes |
Keywords
- Balanced realization
- Descriptor systems
- Hankel singular values
- Periodic systems
- Reachability and observability Gramians
ASJC Scopus subject areas
- Analysis