Title :
On stabilizability and sampling for infinite dimensional systems
Author :
Rosen, I.G. ; Wang, C.
Author_Institution :
Dept. of Math., Univ. of Southern California, Los Angeles, CA, USA
fDate :
10/1/1992 12:00:00 AM
Abstract :
Some questions, either motivated by or related to time sampling, regarding the stabilizability of infinite-dimensional or distributed parameter systems are considered. In particular, these include the characteristics of those systems which are finite rank stabilizable, and the preservation of stabilizability under sampling. A pathological class of systems, which, when sampled, may be rendered unstabilizable by arbitrarily small perturbations in the sampling rate, is identified. The approach taken in establishing these results is based upon a spectral decomposition of the infinitesimal generator of the underlying open-loop semigroup. The results obtained apply to control systems with dynamics described by broad classes of partial and functional differential equations that arise frequently in applications
Keywords :
distributed parameter systems; multidimensional systems; sampled data systems; spectral analysis; stability; distributed parameter systems; dynamics; functional differential equations; infinite dimensional systems; infinitesimal generator; open-loop semigroup; partial differential equations; sampling; sampling rate; spectral decomposition; stability; stabilizability; Control systems; Differential equations; Distributed parameter systems; Hilbert space; Mathematics; Open loop systems; Optimal control; Pathology; Riccati equations; Sampling methods;
Journal_Title :
Automatic Control, IEEE Transactions on
