Abstract
In this note, we propose necessary and sufficient conditions for the asymptotic stability analysis of two-dimensional (2-D) systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions that enable us to analyze the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that, by employing the generalized S-procedure, we can derive smaller size of LMIs so that the computational burden can be reduced.
| Original language | English |
|---|---|
| Pages (from-to) | 1509-1513 |
| Number of pages | 5 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 51 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - Sept 2006 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering