One Design Approach of Positive H∞ Linear Functional Observers

For linear positive systems, one class of linear functional observers is proposed to estimate non-negative system states. The objective is a new design procedure based on $\mathbf{H}_{\infty}$ norm principle. An observer design technique based on the Lyapunov method is given to design the observer parameters where, to get convenient forms of computations, the linear matrix inequality algorithm is formulated, and conditioned by one matrix equality. The resulting functional observer is nonnegative, quadratically stable, converging asymptotically to a prescribed functional state. The design steps are given out by an example to show the validity of the proposed method.