  This contribution proposes a recursive set-membership method for the
ellipsoidal state characterization for discrete-time linear time-varying models
with additive unknown disturbances vectors, bounded by possibly degenerate
zonotopes and polytopes, impacting respectively, the state evolution equation
and the sporadic measurement vectors, which are expressed as linear inequality
and equality constraints on the state vector. New algorithms are designed
considering the unprecedented fact that, due to equality constraints, the shape
matrix of the ellipsoid characterizing all possible values of the state vector
is non invertible. The two main size minimizing criteria (volume and sum of
squared axes lengths) are examined in the time update step and also in the
observation updating, in addition to a third one, minimizing some error norm
and ensuring the input-to-state stability of the estimation error. The author's
papers [1] and [2] were combined into this longer, more comprehensive version.
It includes all the proofs and a few images and is meant to be a support for
the reader. There is no introduction, no conclusion, and no application
examples.
