Frequency domain analysis for stability robustness of multivariable feedback systems

This paper presents techniques for analyzing stability robustness of multivariable control systems. The upper bounds for each element of the allowable perturbation matrices can be obtained whether highly structural information is available or not. Approaching from testing the nonsingularity of a matrix by its eigenvalues instead of using matrix norms, the main algorithm involved is the computation of the spectral radii of certain nonnegative matrices. Due to the fact that any matrix norm is never less than the spectral radius of the same matrix, less conservative results are obtained using our criteria as compared with those obtained by utilizing matrix norms.