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The problem of linear time-varying(LTV) system modal analysis is considered based on time-dependent state space representations,as classical modal analysis of linear time-invariant systems and current LTV system modal analysis under the “frozen-time” assumption are not able to determine the dynamic stability of LTV systems.Time-dependent state space representations of LTV systems are first introduced,and the corresponding modal analysis theories are subsequently presented via a stabilitypreserving state transformation.The time-varying modes of LTV systems are extended in terms of uniqueness,and are further interpreted to determine the system’s stability.An extended modal identification is proposed to estimate the time-varying modes,consisting of the estimation of the state transition matrix via a subspace-based method and the extraction of the time-varying modes by the QR decomposition.The proposed approach is numerically validated by three numerical cases,and is experimentally validated by a coupled moving-mass simply supported beam experimental case.The proposed approach is capable of accurately estimating the time-varying modes,and provides a new way to determine the dynamic stability of LTV systems by using the estimated time-varying modes.