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

Abstract

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 $\mu$ . 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 $\mu$ for the number of scalar constraints, while problems for 2)–4) can be reformulated as a constant-matrix $\mu$ -synthesis problem, which can be approached by $D,G-K$ iteration.