H-INFINITY NORM SENSITIVITY FORMULA WITH CONTROL-SYSTEM DESIGN APPLICATIONS

An analytic formula for the sensitivity of singular value peak variati on with respect to parameter variation is derived. As a corollary, the derivative of the H(infinity) norm of a stable transfer function with respect to a parameter is presented. It depends on the first derivati ve of the transfer function with respect to the parameter. If the tran sfer function has a linear system realization whose matrices depend on the parameter, then an analytic formula for this derivative is derive d, and an efficient algorithm for calculating the H(infinity) norm sen sitivity is described. Examples are given that provide numerical verif ication of the H(infinity) norm sensitivity formula and that demonstra te its utility in designing control systems satisfying H(infinity) nor m constraints.