Linear Fractional Transformations

Abstract

This chapter introduces the linear fractional transformation (LFT), which is a convenient and powerful formulation in control system analysis and controller synthesis. The LFT formulation employs a two-port matrix description linked by a terminator to represent a closed-loop feedback system with two individual open-loop systems. This representation is inherently suitable for MIMO systems. Several examples are given to show how to locate the interconnected transfer function for a given system by using LFT and also how to formulate a control design problem into LFT. Additionally, in order to understand the benefit of utilizing LFT, the relationship between Mason’s gain formulae and LFT will be discussed in this chapter. Inner and co-inner systems are relevant to various aspects of control theory, especially H _∞ control. Definitions of inner and co-inner functions are thus introduced in the last section of this chapter.