A new approach to H_∞ model reduction for positive systems

In this paper, we investigate model reduction for positive linear time-invariant systems in the H_∞ sense. First, the bounded real lemma is further developed to obtain a new characterization of the H_∞ performance, which does not include any product term between the Lyapunov matrix and the parameter of the reduced-order model. Then a new parameterization of a positive reduced-order model is proposed, and accordingly, an iterative algorithm is constructed, which makes use of the coarse reduced-order models resulting from the (generalized) balanced truncation as the initial value to search for a desired positive one. Both continuous- and discrete-time systems are considered in the same framework. Numerical examples clearly show the effectiveness and advantages of the proposed method.