For non-uniformly periodically sampled multirate systems

we derive the corresponding lifted state-space models by using the lifting technique.Furthermore

for multirate systems whose states are measurable

an identification method to estimate the lifted system parameter matrices is given by using the least squares principle;for multirate systems whose states are unmeasurable

the lifted multirate systems are decomposed into some subsystems according to the hierarchical identification principle

and the hierarchical state-space model identification methods are developed

which take causality constraints into consideration.The simulation results indicate that the proposed algorithms are effective.