In this work it is proposed a novel dynamical model of the Lithium-ion batteries intended for diagnosis, prognosis and health-aware control. The proposed model is a particular version of an equivalent electrical circuit and a thermal model. The modeling problem considers that a new battery can be considered as a reference battery with nominal behavior, and the deteriorated one has the same mathematical structure with a multiplicative degradation parameter, considered here to be an input of the system. The battery degradation is considered to simultaneously affect both the capacity of the battery and the value of the internal resistance. The proposed approach considers that just one degradation parameter can absorbs all possible sources of degradation. Experimental data is used to illustrate the proposed battery model and its corresponding degradation parameter estimation. The latter problem is solved by finding the system input (i.e. the degradation parameter) as the solution of a feedback control problem which minimizes the prediction error concerning the terminal voltage. The results also include obtained estimations on temperatures and State of Charge for different battery aging scenarios. Here, we illustrate how a more accurate model of both: the open-circuit voltage and the internal resistance can be used for improving the estimation of the battery aging.