Number theory in science and communication
Number theory in science and communication
Nonlinear approximation theory
Nonlinear approximation theory
Algorithmic information theory
Algorithmic information theory
Introduction to cryptology
Cryptography: an introduction to computer security
Cryptography: an introduction to computer security
H ∞ -optimization and optimal rejection of persistent disturbances
Automatica (Journal of IFAC)
On identification of stable systems and optimal approximation
Automatica (Journal of IFAC)
Robust stabilization: BIBO stability, distance notions and robustness optimization
Automatica (Journal of IFAC)
Information-based complexity and nonparametric worst-case system identification
Journal of Complexity - Special issue: invited articles dedicated to J. F. Traub on the occasion of his 60th birthday
Worst-case control-relevant identification
Automatica (Journal of IFAC) - Special issue on trends in system identification
Robust and optimal control
Feedback Control Theory
Robust input-output stabilization on Z for persistent signals
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
Modelling of linear time-invariant (LTI) systems is studied in an approximate modelling framework motivated by modern robust control theory. As convolution-type LTI systems are represented by their unit impulse responses (i.e. through a sequence of real (complex) numbers), this paper provides also system theoretic results on modelling of sequences and their associated transfer functions. The modelling results derived in this paper are mostly of lethargy type, i.e. they establish limitations in approximate modelling of LTI systems. Non-existence of coprime factorizations is established for a number of different types of LTI systems. This leads to the somewhat surprising conclusion that many LTI systems are not even stabilizable and that an even larger class of LTI systems cannot be well-approximated by rational transfer function models. In addition, it is discussed that often the rate of rational approximation of LTI systems is not essentially better than the rate of approximation in some basis (such as finite impulse response (FIR) models). Furthermore, different definitions of the important finite power signal setup are studied and new results given.