A general theory of linear time-invariant adaptive feedforward systems with harmonic regressors
- 1 November 2000
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 45 (11), 1983-1996
- https://doi.org/10.1109/9.887622
Abstract
Establishes necessary and sufficient conditions for an adaptive system with a harmonic regressor (i.e., a regressor comprised exclusively of sinusoidal signals) to admit an exact linear time-invariant (LTI) representation. These conditions are important because a large number of adaptive systems used in practice have sinusoidal regressors, and the stability and performance of such systems having LTI representations can be completely analyzed by well-known methods. The theory is extended to applications where the LTI conditions do not hold, in which case the harmonic adaptive system can be written as the parallel connection of a purely LTI subsystem and a linear time-varying (LTV) subsystem. An explicit upper bound is established on the induced two-norm of the LTV block, which allows systematic treatment using emerging robust control methods applicable to LTI systems with norm-bounded LTV perturbations.Keywords
This publication has 24 references indexed in Scilit:
- MMIC based phased array radar T/R modulesPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2011
- The LMI control toolboxPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2002
- Wavelet transform based adaptive filters: analysis and new resultsIEEE Transactions on Signal Processing, 1996
- Narrow-band control experiments in active vibration isolationPublished by SPIE-Intl Soc Optical Eng ,1994
- Harmonic generation in adaptive feedforward cancellation schemesIEEE Transactions on Automatic Control, 1994
- Linear Matrix Inequalities in System and Control TheoryPublished by Society for Industrial & Applied Mathematics (SIAM) ,1994
- Comparison and extensions of control methods for narrow-band disturbance rejectionIEEE Transactions on Signal Processing, 1992
- A multiple error LMS algorithm and its application to the active control of sound and vibrationIEEE Transactions on Acoustics, Speech, and Signal Processing, 1987
- State-space analysis of the adaptive notch filterProceedings of the IEEE, 1986
- Adaptive noise canceling applied to sinusoidal interferencesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1977