Obtaining uniform singular values of augmented systems using LQG/LTR

Well-developed methods exist for obtaining matched bounds on the singular values at either low or high frequencies for general MIMO systems using LQG/LTR design techniques. For systems that have been augmented with additional free-integrator dynamics, it has previously been shown that one can match the bounds at low frequencies and high frequencies, simultaneously. This paper presents a method for obtaining matched upper and lower bounds on the singular values over all frequencies for the target loop. The procedure requires that the augmented systems have free integrators acting on each of the inputs. An example is included which illustrates the technique and demonstrates how to utilize preexisting free integrators within the system.