Chain Scattering Descriptions

  • Mi-Ching Tsai
  • Da-Wei Gu
Part of the Advances in Industrial Control book series (AIC)


The chain scattering-matrix description (CSD) of a two-port network, first introduced in Chap. 2, originated from the conventional electrical circuit theory. In contrast to the LFT, the CSD developed in the network circuits provides a straightforward interconnection in a cascaded way. The CSD can transform an LFT into a two-port network connection and vice versa. Thus, many known results which have been developed for a two-port network can then be used in control system analysis and synthesis. Due to its benefits of describing a linear system, the CSD was later extended to the design of robust control systems [1, 2], where different structures of the CSD were investigated. In this chapter, the CSD will be formally defined and explored for transformations and the descriptions of state-space realizations. The J-lossless and dual J-lossless systems are defined in this chapter. J-lossless and dual J-lossless both play an important role in the CSD control system manipulations, analysis, and synthesis. In particular, the properties of J-lossless and dual J-lossless are essential in synthesizing H (sub)optimal controllers using the CSD approach.


Chain Scattering State-space Realization Star Product Coprime Factorization Lower Triangle Matrix 
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  1. 1.
    Green M (1992) H controller synthesis by J-lossless coprime factorization. SIAM J Control Optim 30:522–547CrossRefzbMATHMathSciNetGoogle Scholar
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    Kimura H (1997) Chain-scattering approach to H control. Birkhäuser, BostonCrossRefzbMATHGoogle Scholar
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    Redheffer RM (1960) On a certain linear fractional transformation. J Math Phys 39:269–286MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Mi-Ching Tsai
    • 1
  • Da-Wei Gu
    • 2
  1. 1.Department of Mechanical EngineeringNational Cheng Kung UniversityTainanTaiwan
  2. 2.Department of EngineeringUniversity of LeicesterLeicesterUK

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