  This paper considers the design of robust state observers for a class of
slope-restricted nonlinear descriptor systems with unknown time-varying
parameters belonging to a known set. The proposed design accounts for process
disturbances and measurement noise, while allowing for a trade-off between
transient performance and sensitivity to noise and parameter mismatch. We
exploit a polytopic structure of the system to derive
linear-matrix-inequality-based synthesis conditions for robust
parameter-dependent observers for the entire parameter set. In addition, we
present (alternative) necessary and sufficient synthesis conditions for an
important subclass within the considered class of systems and we show the
effectiveness of the design for a numerical case study.
