A new positive linear functional filters design for positive linear systems

This paper is concerned with a new time domain design of a positive functional filters for linear time-invariant continuous-time positive multivariable systems, affected by bounded disturbances. Roughly speaking, a positive system is a dynamic system whose output remains in the non-negative orthant whenever the initial state and the input is non-negative. The order of the proposed filter is equal to the dimension of the vector to be estimated. This new approach is based on the unbiasedness of the filter using a Sylvester equation; then the problem is solved via Linear Matrix Inequalities (LMI) to find the optimal gain implemented in the positive filter design. All filter matrices are designed, such that the dynamics of the estimation error is positive and asymptotically stable. A numerical example is given to illustrate our approach.