Finite-Time State Estimation of Discrete-Time Linear Systems with Some Extensions. Application to Steering Lateral Vehicle Model

This paper presents novel exact finite-time estimation algorithms for linear discrete-time systems with extension to singular systems, under specific rank conditions. The proposed estimation algorithms are more general than the well-known deadbeat observers, which can provide finitetime estimation. Two new estimation schemes are proposed; the first scheme provides a direct and explicit estimation algorithm based on the use of delayed outputs, while the second scheme uses two combined asymptotic observers to recover in a finitetime the exact solution of the system. The effectiveness of the developed estimators is shown through application to a steering controlled lateral vehicle system where all states are estimated from look-ahead distance measurement.