The subject of this paper is online identification of systems described by linearly parametrized models, under the assumption that the parameters in question are slowly time varying, and with the requirement that the normal operation of the system is left completely undisturbed by the estimation procedure. A Lyapunov-based parameter estimator design for a class of LP systems is presented, assuming that we have no control over any of the system inputs, including control inputs. The estimation is guaranteed to converge provided good knowledge of extreme scenarios is available and provided certain observability-like requirements, derived in the paper, are met. The proposed design procedure is interpreted in the light of observer design for an ‘envelope’, augmented system where the parameters to be estimated are treated as slow state variables. Illustrative numerical examples follow; Good performance is observed both for the idealized case and for the case where sensor noise is present.