Necessary and sufficient conditions for LTI representations of adaptive systems with sinusoidal regressors

This paper establishes necessary and sufficient conditions for an adaptive system with a sinusoidal 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, convergence and robustness properties of systems having LTI representations can be completely analyzed by well-known methods.