Robust Control Design Using Structured Singular Values

Abstract

As we showed in the previous chapter there are two main limitations in connection with H_∞ control theory. Probably the most important is that we can only handle full complex perturbation structures Δ(s) ∈ C^{n × m} non-conservatively in an H_∞ robustness test. The other main limitation is that the robust performance problem can only be considered conservatively even for a full complex perturbation set because performance and robustness cannot be separated in the H_∞ framework. The conservatism introduced depends on the applied perturbation model and the condition number of the plant. In this chapter we shall shown that both these limitations may be overcome using the structured singular value μ.