Positive unknown inputs functional observers new design for positive linear systems

Abstract

This paper deals with the problem of designing positive functional observers for positive linear systems subject to unknown inputs. The order of the designed observer is equal to the dimension of the functional to be estimated. The designed functional observer is always nonnegative at any time and converges asymptotically to the real functional state vector. In fact, we propose a new positive reduced order observer for positive linear systems affected by 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 functional observer design is given. Finally, numerical example and simulation results are given to illustrate the effectiveness of the proposed design method.