Abstract
The finite-horizon ℓ2-induced norm evaluation problem of discrete-time switched linear systems is considered in this paper. The set of worst-case switching laws is characterized, which is a subset of the whole set of switching laws under consideration. Based on the properties of the worst-case switching law set, a low-complexity complete solution to the ℓ2-induced norm evaluation problem is provided for general switched linear systems. It is shown that under the assumption of exponential stability, the finite-horizon ℓ2-induced norm monotonically converges to the infinite-horizon norm, and the volume of the worst-case switching law set gradually becomes constant as the time horizon approaches infinity. Some numerical properties of the worst-case switching law set are also exploited. A numerical example is presented to illustrate the proposed results.
| Original language | English |
|---|---|
| Pages (from-to) | 2517-2524 |
| Number of pages | 8 |
| Journal | Automatica |
| Volume | 49 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - Aug 2013 |
| Externally published | Yes |
Keywords
- Discrete-time switched linear systems
- Worst-case switching law set