Model reduction and ℓ1-gain analysis for two-dimensional positive systems

In this paper, for the two-dimensional (2-D) positive linear system, model reduction problem is tackled and the ℓ1-gain performance is also discussed. By constructing suitable co-positive Lyapunov function, criteria are obtained for the considered 2-D positive model to be asymptotically stable with given ℓ1-gain index. Then, specific design schemes are given to acquire the estimator matrix parameters for the reduced-order 2-D system. Simulation example is also given to provide effectiveness of the proposed method.

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