T-2-4-1 Design of the Well-Conditioned Observer Using the Non-Normality Measure

In this paper, the well-conditioned observer is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. An L_2-norm based condition number of the observer eigenvector matrix has been proposed as a main index in the observer performance. For the well-conditioned observer design, the non-normality measure and the observability condition of the observer matrix are considered. These two constraints are specified into the desirable observer gain region that satisfies a small condition number and a stable observer. The observer gain selected in this region guarantees well-conditioned estimates in the observer performance. In this study, well-conditioning properties are investigated regarding the Luenberger observer and the Kalman filter for 2^ order systems. In designing Kalman filters, the covariance ratio between the process noise and the measurement noise is shown to be a design variable and its effect on the condition number is characterized.