Positive Unknown Input Observer For Positive Linear Systems
For control theorists working on positive systems, this solves the previously open problem of unknown input estimation, though the approach is incremental as it extends existing observer theory.
This paper presents the first design of positive unknown input observers (PUIO) for positive linear systems, enabling state estimation despite unknown inputs or disturbances. The proposed method uses LMI-based stabilization and conditions on generalized inverse positivity.
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.