An Ellipsoidal Predictor–Corrector State Estimation Scheme for Linear Continuous-Time Systems With Bounded Parameters and Bounded Measurement Errors

For linear time-invariant dynamic systems with exactly known coefficients of their system matrices for which measurements with bounded errors are available at discrete time instants, an optimal polygonal state estimation scheme was recently published. This scheme allows for tightly enclosing all possible state trajectories in presence of uncertain, but bounded, system inputs which may be varying arbitrarily within in their bounds. Moreover, this approach is also capable of accounting for uncertainty related to the measurement time instants. However, the drawback of this polygonal technique is its rapidly increasing complexity for larger system dimensions. For that reason, the polygonal state enclosures are replaced by a computationally less expensive, but nearly optimal, ellipsoidal enclosure technique in this paper. Numerical simulations for representative benchmark examples focusing both on applications with precisely known and uncertain parameters conclude this contribution.