Spectral Radius Design for Robust Multivariable Control

A sufficient condition for robust stability and disturbance rejection in multivariable control systems is presented. The condition is a bound on the spectral radius of a weighted set of closed loop transfer function matrices. Frequency dependent weighting matrices are determined from structured bounds on plant uncertainties and performance specifications. For certain clases of robust control problems, including nonminimum phase systems, the spectral radius has a particularly simple form that leads directly to graphical methods for control synthesis. Though the bounds are conservative, the technique does lead to simple graphical interpretations. This is illustrated for systems subject to additve plant perurbations and with performance constraints on both the control input and output error.