Necessary and Sufficient Conditions on the Observability and Identifiability of Linear Systems

A new representation of linear time-invariant systems is presented. This representation enables to generate necessary and sufficient conditions on the simultaneous state observability and parameters identifiability of linear time-invariant systems. Sufficient conditions derived from the necessary and sufficient conditions are weaker than the well known persistent excitaion conditions in the existing least square schemes. Namely, a sum of n distinct exponentials in the input to the system is almost always sufficient This is half of the quantity required in the common existing least square algorithms. These conditions apply to estimation in open and closed loop without further restrictions. Simulation results demonstrate the performance of estimation with this new approach.