#### Conference Contribution

## Continuous-Time Model Identification and State Estimation Using Non-Uniformly Sampled Data

### Rolf Johansson

##### Abstract

This contribution reviews theory, algorithms, and validation results for system identification of continuous-time state-space models from finite input-output sequences. The algorithms developed are autoregressive methods, methods of subspace-based model identification and stochastic realization adapted to the continuous-time context. The resulting model can be decomposed into an input-output model and a stochastic innovations model. Using the Riccati equation, we have designed a procedure to provide a reduced-order stochastic model that is minimal with respect to system order as well as the number of stochastic inputs, thereby avoiding several problems appearing in standard application of stochastic realization to the model validation problem. Next, theory, algorithms and validation results are presented for system identification of continuous-time state-space models from finite non-uniformly sampled input-output sequences. The algorithms developed are methods of model identification and stochastic realization adapted to the continuous-time model context using non-uniformly sampled input-output data. The resulting model can be decomposed into an input-output model and a stochastic innovations model. For state estimation dynamics and Kalman filters, we have designed a procedure to provide separate continuous-time temporal update and error feedback update based on non-uniformly sampled input-output data.

In *Proc. 19th International Symposium on Mathematical Theory of Networks and Systems*,
July 2010.

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