Some results in nonlinear QFT

Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an 'equivalent' family of linear plants. Th e problem is then finding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradi tion of linearization approaches to nonlinear control (describing functions , extended linearization, etc.) which have been found to be quite effective in a wide range of applications. In recent work, the authors have develope d an alternative function space method for the derivation and validation of nonlinear QFT that has clarified and simplified several important features of this approach. In particular, single validation conditions are identifi ed for evaluating the linear equivalent family, and as a result, the nonlin ear QFT problem is reduced to a linear equivalent problem decoupled from th e linear QFT formalism, In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circum vention of problems encountered in the application of this approach. Copyri ght (C) 2001 John Wiley & Sons, Ltd.