A generalized sensitivity approach to feedback systems in Hilbert space

Abstract

A generalized sensitivity study of physical systems in Hilbert space, which involve any feedback law, is presented. Some of the results previously obtained for the class of physical systems which are described by ordinary differential equations appear as special cases. Situations where the systems involve time delays or time lags or distributed-parameters, etc., can be treated by the present theory. The results are based on a general model of physical systems consisting of a left-hand side linear (or non-linear) operator acting on the systems state and of a right-hand aide nonlinear operator acting on the state, the control input, and a set of unknown parameters. A computational method for solving the resulting equations is suggested which possesses second-order convergence and proved to be successful in a wide range of applications.