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A general theory of linear time-invariant adaptive feedforward systems with harmonic regressors

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1 Author(s)
Bayard, D.S. ; Jet Propulsion Lab., California Inst. of Technol., Pasadena, CA, USA

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:45 ,  Issue: 11 )