THE V-TRANSFORM - A TOOL FOR ANALYSIS OF CONTROL-SYSTEMS ROBUSTNESS WITH RESPECT TO DISTURBANCE MODEL UNCERTAINTY

This work is motivated by the need for tools for the analysis of distu rbance model uncertainty in feedback control systems. Such tools are d eveloped in this paper for the case where the disturbance is modeled a s the output of a first-order filter which is driven by white noise an d whose bandwidth, (omega(d)) and gain, K, are uncertain. An analytica l expression for the steady-state output variance as a function of ome ga(d) is derived: This function is referred to as a V-transform, and i s denoted by V(G)(omega(d)), where G(s) is the closed-loop transfer fu nction from disturbance to output. Properties of V-transforms are inve stigated and the notions of disturbance gain margin and disturbance ba ndwidth margin, both measures of robustness with respect to disturbanc e model uncertainty, are introduced. Using these new tools, it is show n that there is a fundamental robustness performance limitation if the plant has nonminimum-phase zeros, but no such limitation in the minim um-phase case.