Stabilization of multivariable systems with constrained control structure

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