Decompositions of Proper Systems

  • Ben M. Chen
  • Zongli Lin
  • Yacov Shamash
Part of the Control Engineering book series (CONTRENGIN)


We present in this chapter the structural decomposition of linear time-invariant systems as represented by a matrix triple or a matrix quadruple. In order to make the presentation easier to follow, we will start with the structural decomposition of single-input and single-output (SISO) systems. It will be followed by a detailed construction of the structural decomposition for a general strictly proper multi-input and multi-output (MIMO) system. The decomposition of a general nonstrictly proper MIMO system will then be given together with detailed proofs of system properties revealed under the decomposition. We will conclude the chapter with the structural decomposition of general discrete-time systems.


MIMO System Structural Decomposition Proper System SISO System Jordan Canonical Form 
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Copyright information

© Birkhäuser Boston 2004

Authors and Affiliations

  • Ben M. Chen
    • 1
  • Zongli Lin
    • 2
  • Yacov Shamash
    • 3
  1. 1.Dept. of Elec. & Comp. EngineeringNational University of SingaporeSingapore
  2. 2.Dept. of Elec. & Comp. EngineeringUniversity of VirginiaCharlottesvilleUSA
  3. 3.College of Eng. and Appl. SciencesState University of New York at Stony BrookStony BrookUSA

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