A hyperstable ALE for tracking complex cisoids is presented . The ALE incorporates an adaptive IIR Filter , with the convergence of the filter being conditional on the overall system being 'passive' . The passivity of the system depends on the location of the input cisoid frequencies, and it is shown that for the case of upto two cissoids, the system is passive for all distinct frequencies. For the case of larger number of cissoids, the system is passive for certain ranges of the cisoid frequencies . Simulations are also given to back up the theoretical results .