State and parameter estimation for overall systems

Here the joint problem of state estimation and parameter identification for a class of semilinear system is reframed into a enlarged form called overall system which incorporates the unknown parameters to be identified as new states with constant values. Then the problem is transformed into just state observation of the overall system. Two theorems which establishes necessary and sufficient conditions for linear observability of the overall system are shown. A result which relates the overall system with the characteristic polynomial of the original system is also presented