POSITIVE OBSERVATION PROBLEM FOR LINEAR TIME-LAG POSITIVE SYSTEMS

This paper deals with the problem of positive observation for linear positive time-lag systems for which the states take nonnegative values whenever the initial conditions are nonnegative. That is, the design of positive observers (possibly with time-lag) which guarantee nonnegative estimates of the current states of linear time-lag positive systems. The provided conditions for the existence of a positive observer (extended Luemberger-type) are necessary and sufficient and solvable in terms of Linear Programming (LP). Also, it is shown that it is no longer possible to stabilize any unstable time-lag positive system by using extended Luenberger-type positive observers.