Optimum feedback patterns in multivariable control systems

The following problem is considercd: 'Given a multivariable system with m inputs and r outputs and an r×m matrix whose non-negative (i, j)th element represents the cost of setting up a feedback link from the jth output to the ith input, sind a set of feedback links with minimum total cost, which does not give rise to sixed modes'. Utilizing the graph-theoretic characterization of structurally sixed modes, the problem is decomposed into two subproblems, which are then solved by using concepts and results from network theory. A combination of the optimum solutions of the subproblems provides a suboptimal solution to the original problem.