Structured singular value analysis for real parameter variations

Abstract

The structured singular value approach to multivariable robustness analysis gives margins that are conservative. Some of this conservatism is due to the fact that the structured singular value margin is based on singular value measurement of all possible uncertainties in the system, including complex valued uncertainties. Many uncertainties in realistic systems can only vary in a strictly real valued sense; for such systems, the structured singular value analysis technique evaluates uncertainties that are not physically possible. This paper introduces an upper bound approximation for real structured uncertainty analysis which is less conservative than the structured singular value method for determining a robustness margin for multivariable systems with real uncertainties. It also expands the theory to encompass evaluation of both strictly real and complex uncertainty structures in the same system. An efficient evaluation method for the resultant robustness margin is presented. The reduction of conservatism is demonstrated through analysis of the yaw-roll autopilot for a typical hypervelocity vehicle design.