On Informative State Vectors for Discrete Dynamic Estimation in Switched Systems Using the Model-Based Minimum Distance Method

This technical note addresses the discrete dynamic estimation problem in switched linear systems using the model-based minimum distance method (MB-MDM). Prior work has shown that, for this method, the state vector must be sufficiently far from the origin to guarantee an accurate estimation of the discrete dynamic, thereby confirming inherent conflicts between discrete dynamic estimation and feedback control objectives in switched systems. To enhance the accuracy of the MB-MDM, this work focuses on characterizing the region of state vectors that enable exact discrete dynamic estimation, termed informative state vector (ISV). The contributions of this paper are twofold. Firstly, a necessary and sufficient condition based on linear matrix inequalities is derived to determine whether a state vector is informative, revealing that ISV must lie outside a specific ellipsoid. Based on this observation, an ellipsoid-based approach is then proposed to estimate the ISV region.