Positive Unknown Input Observer Design for Positive Linear Systems

Positive systems are important class of dynamic systems with impressive properties. The response of such systems to positive initial conditions and positive inputs remain in the nonnegative orthant of the state space. Although positive observers have been designed for positive systems, they are unable to estimate the states when unknown inputs or disturbances are present in the systems. This paper is a first attempt to design positive unknown input observers (PUIO) for positive linear systems. The structural constraints on observer parameters make the design task cumbersome. However, with the aid of a positive stabilization scheme via LMI and by imposing conditions on positivity of the generalized inverse associated with a certain design matrix, we provide a reliable procedure for the design of PUIOs.