Design of Positive Observers for Positive Linear Time-delay Systems

The proposed paper addresses problem of positive observer design for positive time-delay systems subject to unknown inputs. We focus on the design of positive observers with time-delay, for systems which the states take nonnegative values whenever the initial conditions are nonnegative. The designed observer should guarantee both the positivity of the estimated state and the asymptotically convergence to the true state vector. In fact, we propose a new positive observer for positive linear time-delay systems subject to unknown inputs. The proposed procedure is based on the positivity of an augmented system composed of dynamics of both considered system and proposed observer and also, on the unbiasedness of the estimation error by the resolution of Sylvester equation; then existence conditions of such observers are formulated in terms of linear programming (LP) problem, where we use the Perron-Frobenius theorem applied to Metzler matrices. An algorithm that summarizes the different steps of the proposed positive unknown inputs observer design is given.