UC San Diego

Algorithms for simultaneous input and state estimation (SISE algorithms) that are optimal in the minimum-variance unbiased sense have been in development for decades. The stability of such algorithms is not guaranteed. For time invariant systems, this thesis derives necessary and sufficient stability conditions. In the square case, where the number of inputs equals the number of outputs, the exact positions of the algorithm’s poles are established. In the non-square case, the derived stability condition is formulated as a detectability condition. Those necessary and sufficient conditions are generalized to sufficient only conditions for the time varying case. Lastly, the effect of delay in the system under consideration on the SISE algorithm is explored. A general method, inspired by fixed lag smoothing, is proposed to handle cases where a general delay is present.