Stability margins of diagonally perturbed multivariable feedback systems

For diagonally perturbed linear time-invariant multivariable feedback systems, the problem of finding an improved characterization of stability margin is examined. Although exact calculation of margins is found to be impractical, a readily computable lower bound for diagonally, perturbed systems is developed using Perron-Frobenius nonnegative matrix results. The present theory improves upon the existing singular-value stability margin theory, providing a simple constructive method for determining previously unspecified norm weighting parameters (i.e., scaling factors) so as to minimize the conservativeness of stability margin bounds.