Parallel structured network for solving balanced realization problems

Given a state space description of a linear system, the balanced realization problem is to find a similarity transformation for the state variables. This transformation must transfer both the system energy matrix and the output energy matrix into diagonal form. In this paper a novel parallel structured network (PSN) is constructed to solve this problem. The three possible forms of realization, which are defined in the literature can be obtained using the PSNs. Furthermore, the fourth one, defined and found here, is new, and has not been mathematically defined in earlier work