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Transfer function matrix

Transfer function matrix

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© The Institution of Electrical Engineers
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Given a multivariable system, it is proved that the numerator matrix N(s) of the transfer function evaluated at any system pole either has unity rank or is a null matrix. It is also shown that N(s) evaluated at any transmission zero of the system has rank deficiency. Examples are given for illustration.

Inspec keywords: poles and zeros; linear systems; transfer functions; multivariable control systems; matrix algebra

Other keywords: system pole; linear system; transfer function; multivariable system; numerator matrix; transmission zero; control theory

Subjects: Multivariable control systems; Control system analysis and synthesis methods

References

    1. 1)
      • E.J. Davison , S.H. Wang . Properties and calculation of transmission zeros of linear multivariable systems. Automatica , 643 - 658
    2. 2)
      • S.H. Wang , E.J. Davison . A new invertibility criterion for linear multivariable systems. IEEE Trans. , 538 - 539
    3. 3)
      • R.A. Frazer , W.J. Duncan , A.R. Collar . (1938) , Elementary matrices.
    4. 4)
      • H. Seraji . Cyclicity of linear multivariable systems. Int. J. Control , 497 - 504
    5. 5)
      • H. Kwakernaak , R. Sivan . (1972) , Linear optimal control systems.
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