A Computational Framework

The main robustness result of the previous chapter is a both necessary and sufficient condition for robust stabilization of a sampled-data system to structured LTI perturbations. The condition is given in terms of the structured singular value of the sampled-data system frequency response µ _{Δ LTI} (M(ejω)) evaluated on the unit circle. The capability to use this stability test therefore relies on the ability to effectively evaluate the structured singular value of the infinite dimensional operator M(ejω). This chapter is aimed at developing a computational framework that addresses this task. The approach used is to obtain bounds: we construct a family of upper and lower bounds for µ _{Δ LTI} (M(ejω)) whose members converge to µ _{Δ LTI} (M(ejω)). The resulting computational procedure is one in which the accuracy of the bounds for µ _{Δ LTI} (M(ejω)) can be systematically improved at the cost of additional computational effort.