Divergence of the stationary Kalman filter for correct and for incorrect noise variances

The convergence properties of the estimation error covariancefor the Kalman filter are analysed. Criteria are derived forconvergence or divergence of the estimation error if the time-invariantKalman filter is used, possibly designed for incorrect noisedata. The analysis uses recently developed convergence resultsfor the solution of the matrix Riccati differential equation.     

On the Stability of Numerical Integration Routines for Ordinary Differential Equations

Numerical integration methods for the solution of initial valueproblems for ordinary vector differential equations may be modelledas discrete time feedback systems. The stability criteria discoveredin modern control theory are applied to these systems and criteriainvolving the routine, the step size and the differential equationare derived. Linear multistep, Runge-Kutta, and predictor-correctormethods are all investigated.