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
Robust and optimal control
Stability and Robustness of Multivariable Feedback Systems
Stability and Robustness of Multivariable Feedback Systems
Squared and absolute errors in optimal approximation of nonlinear systems
Automatica (Journal of IFAC)
Brief On robustness in system identification
Automatica (Journal of IFAC)
On linear models for nonlinear systems
Automatica (Journal of IFAC)
LTI approximation of nonlinear systems via signal distribution theory
Automatica (Journal of IFAC)
Measuring a linear approximation to weakly nonlinear MIMO systems
Automatica (Journal of IFAC)
On robustness in control and LTI identification: Near-linearity and non-conic uncertainty
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
Linear time-invariant (LTI) modelling of nonlinear finite impulse response (NFIR) systems is studied from a control point of view. Nearly linear NFIR systems and their control-relevant properties are analysed in detail. The main modelling interest is in the analysis of least squares (LS) LTI identification when the true system is an NFIR system, which is possibly nearly linear. Linearization is used for comparison purposes as the second LTI modelling technique. Nearly linear systems provide a natural generalization of LTI systems to include nonlinearities that allow globally good LTI approximations, while at the same time, such nonlinearities can have a very dramatic effect on the local characteristics of the system. Several control-oriented examples illustrate the possible weaknesses and strengths of the studied LTI modelling techniques. Linearization is found to be especially vulnerable to the presence of even very small, only locally significant, nonlinearities. LS estimation can largely avoid such difficulties, but input design becomes a more critical issue than in standard linear estimation theory. Certain counter-intuitive properties of commonly used input-output stability notions, such as @?"2 stability, are discussed via the concept of near-linearity.