Positive functional filters synthesis for positive linear systems

This paper deals with the problem of positive functional H-infinity filtering for positive linear systems subject to both bounded disturbances and unknown inputs. The order of the designed H-infinity filter is equal to the dimension of the functional to be estimated, that can be useful for control purpose for example. We focus on the design of positive filters which guarantee that the functional (of the state) is always non-negative at any time and converges to the real functional state by minimizing the effect of the disturbances on the estimation error. In fact, we propose a new positive reduced order H-infinity filter for positive linear systems for which the states remain in the non-negative orthant of the state space, subject to both disturbances and unknown inputs. This paper is a first attempt to design positive unknown inputs functional H-infinity filter for such positive linear systems. The proposed approach is based on the positivity of an augmented system composed of dynamics of both considered system and proposed filter, on the unbiasedness of the estimation error by the resolution of Sylvester equation; then we derive conditions for the establishment of such filters in terms of an optimization problem. An algorithm that summarizes the different steps of the proposed positive functional H(infinity )filter design is given. Finally, numerical example and simulation results are given to showcase the effectiveness of the proposed design method.