Linear fractional transformations

Mi Ching Tsai, Da Wei Gu

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish
Title of host publicationAdvances in Industrial Control
PublisherSpringer International Publishing
Number of pages33
Publication statusPublished - 2014 Jan 1

Publication series

NameAdvances in Industrial Control
ISSN (Print)1430-9491
ISSN (Electronic)2193-1577

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Industrial and Manufacturing Engineering


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