Tracking the state-of-charge and state-of-health presently attracts much attention as they are important evaluation indexes for energy storage systems diagnosis and prognosis in electric vehicles and smart grids. This paper presents a hybrid state-of-charge and state-of-health estimation technique according to adaptation of parameters in an equivalent circuit model and a Lyapunov-based adaptation law. The online adaptation of the equivalent circuit model is employed to maintain accurate estimations by capturing battery age-dependent dynamics. The Lyapunov-based adaptation law is employed to enable the production of internal battery state and age-dependent parameters estimations using only battery terminal voltage and noisy current measurements. Though parameters vary with aging, temperature or other factors, accurate estimations are still achieved without prior knowledge of battery parameters. Besides, the stability of the proposed observer can also be guaranteed by Lyapunov direct method. The proposed method is verified using data collected over randomized discharge profiles. Experimental results highlight the high estimation accuracy and robustness of the proposed model and technique.