Approaches to Determining Box Consistent Parameter Sets for Polytopic Output Constraints on Linear Fractional Models Using Structured Singular Values

This technical note considers the problem of maximizing the volume of a box of parameters that satisfy polytopic output constraints for linear fractional models using the structured singular value μ. In particular, four kinds of boxes are considered: 1) a hypercube centered at a specified location; 2) a freely located hypercube; 3) a freely located box of free shape; and 4) a freely located box of free shape and rotation. It is found that the problem for 1) can be solved by computing μ for the number of scalar constraints, while problems for 2)-4) can be reformulated as a constant-matrix μ-synthesis problem, which can be approached by D, G - K iteration.