Dear Poom,

    Conventional state space models are founded on Gaussian assumptions.   However, if you wanted to model pulse and step functions as one-off events, you could add outlier (blip) dummies or step (level change) dummies to the measurement model of the system.  Such event indicators have been discussed in the works of Commanduer and Koopman 's Introduction to State Space Time Series Analysis (2007) and Andrew C. Harvey's Forecasting Structural Time Series and the Kalman Filter(1989) dealing with modeling time series with the Kalman filter.  This ccapability has been incorporated in the Stamp software of Koopman, Harvey, Doornik, and Shephard. 

     Both works  show how an input series may be included as a fixed or stochastic regressor in the model.

      I Hope this helps,

         Robert

I beleve you are looking for introductory material and/or simple formulations.

The link below might help you.

http://lpsa.swarthmore.edu/Transient/TransInputs/TransStep.html