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Positive systems can be used as mathematical models for many practical systems, such as biological systems, communication networks, and interconnected systems. In this letter, we propose proximal alternating linearized minimization (PALM) and PALM-like algorithms to determine the nearest discrete-time linear positive system to a given system, with the same order as that of the considered system. Global convergence of the PALM algorithm to a critical point of the considered objective function is ensured by using the Kurdyka-&#x0141;ojasiewicz and semi-algebraic properties. Numerical experiments are performed to compare the PALM and PALM-like algorithms.

Construction Methods of the Nearest Positive System