Abstract
It is well known that a finite-dimensional output space implies limitations on the systems properties, like observability and detectability. In this paper we extend this result for infinite-dimensional output spaces, under the condition that the output operator is relatively compact. We show that if this holds, and the system is exactly observable in finite-time, then the inverse of the infinitesimal generator must be compact. By means of an example we show that this result does not hold for exact observability in infinite-time. Using the Hautus test, we obtain spectral properties of the generator for this case. A consequence of this result is that if the system is exponentially detectable, then the unstable part of the spectrum consists of only point spectrum with finite multiplicity.
Original language | English |
---|---|
Pages (from-to) | 672-685 |
Number of pages | 14 |
Journal | SIAM journal on control and optimization |
Volume | 49 |
Issue number | 2 |
DOIs | |
Publication status | Published - May 2011 |
Keywords
- Observability
- Stabilizability
- Relative compact output operator
- Hautus test