Observability of quasimonotone systems

Observability is discussed of quasimonotone dynamic systems determined in a positive cone of the Euclidean space. Conditions are provided for existence of operators that associate nonnegative functions integrated to the $p$-th power with points in a positive cone of the Euclidean space. A straightforward way to solve the observation problem in the Luenberger sense is provided. For a range of observers the existence of optimal observers is proved.