Fiedler Linearizations for Higher Order State-Space Systems

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Higher Order System, System Matrix, Transfer Function, Zero, Zero Direction, Matrix Polynomial, Eigenvalue, Eigenvector, Matrix Pencil, Linearization, Fiedler Pencil.
65F15, 15A18, 15B57, 15A22.


Consider a higher order state space system and associated system matrix S(?). The aim of this paper is to linearize the higher order system preserving system characteristics. That is, we derive a linearized state space system of the given higher order system preserving system characteristics(e.g., controllability, observability, various zeros and transfer function) for analysis of higher order systems which gives the solution for higher order system. We study recovery of zero directions of higher order state space system from those of the linearizations. That is, the zero directions of the transfer functions associated to higher order state space system are recovered from the eigenvectors of the Fiedler pencils without performing any arithmetic operations.


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How to Cite

Behera, N. (2022). Fiedler Linearizations for Higher Order State-Space Systems. The Journal of the Indian Mathematical Society, 89(3-4), 237–261.
Received 2020-07-27
Accepted 2022-02-16
Published 2022-08-23



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