Analysis and synthesis of nested feedback systems

The H_∞-loopshaping framework is extended to the design of nested (or cascaded) feedback systems consisting of an inner and an outer loop. Three robust stability margins are defined for such systems and an inequality relating them obtained for the case when the inner loop is implemented in observer form. This motivates the introduction of two synthesis algorithms which are compared with a sequential approach in the design of a cascade-limiter for the Quanser Helicopter experiment. By establishing an equivalence between normalized coprime factor uncertainty and a combination of output multiplicative and input inverse multiplicative uncertainty, it is possible to demonstrate in what sense the new compensators are superior to the one obtained by the sequential method.