Optimal observers for time varying linear systems

A method is presented for generating the optimal control of a linear system from measurements of the system input and output. The systems considered are n-th order, time invariant or time varying forced linear systems which are restricted to be bounded and uniformly completely state reconstructible. The control is generated from an estimate of the state vector which is obtained from an observer. The observer dynamics are derived from an optimal estimation formulation which is closely related to the concept of observability. Asymptotic stability of the observer is demonstrated and the effects of initial errors are considered. The result is a practical method of estimating the state of a linear system from noiseless measurements of the input and output. Additionally, theoretical results are obtained concerning the existence of observers for time varying linear systems.