Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method

Full Text (PDF, 179KB), PP.1-7

Views: 0 Downloads: 0


Qiang. Ma 1,*

1. School of Power and Energy Engineering, Wuhan University of Technology, Wuhan, China

* Corresponding author.


Received: 23 Dec. 2010 / Revised: 6 Feb. 2011 / Accepted: 10 Mar. 2011 / Published: 8 Apr. 2011

Index Terms

Nonlinear systems structural controllability, transfer function, non-commutative ring, polynomial ring


In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix) of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.

Cite This Paper

Qiang Ma, "Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method", International Journal of Modern Education and Computer Science(IJMECS), vol.3, no.2, pp.1-7, 2011. DOI:10.5815/ijmecs.2011.02.01


[1]C.T. Lin, “Structural controllability,” IEEE Trans. AC-19, pp. 201-208, 1974.
[2]R.W.Shields and J.B. Pearson, “Structual controllability of multiinput linear systems,” IEEE Trans. AC-21, pp. 203-212, 1976.
[3]J.L. Willems, “Structural controllability and observability,” Syst Contr Lett. pp.5-12, 1986.
[4]T. Yamada and D.G. Luenberger, “Generic properties of column-structured matrices,” Linear Algebra Appl. 65, pp. 186-206, 1985.
[5]K. Murota, “On the degree of mixed polynomial matrices,” SIAM J Matrix Anal Appl. 20, pp. 196-227, 1998.
[6]K.S. Lu and J.N. Wei, “Rational function matrices and structural controllability and observability,” IEE Proceedings-D, 138, pp. 388-394, 1991.
[7]K.S. Lu and J.N. Wei, “Reducibility condition of a class of rational function matrices,” SIAM J Matrix Anal Appl.15, pp. 151-161, 1994.
[8]G. Fradellos, M. Rapanakis and F.J. Evans, “Structural controllability in non-linear systems,” Inter. J. Systems Science, No.8, pp. 915-932, 1977.
[9]Y. Zheng and L.Cao, “Transfer function description for nonlinear systems,” Journal of East China Normal University(Natural science), vol 2, pp. 15-26, 1995.
[10]Y.Zheng, J. Willems and C Zhang, “A polynomial approach to nonlinear system controllability,” IEEE Transactions on Automatic Control, vol. 46, pp. 1782–1788, 2001.
[11]M. Halas and Ü. Kotta, “Extension of the concept of transfer function to discrete-time nonlinear control systems,” In European control conference, Kos, Greece, 2007.
[12]M.Halas, “Ore algebras: A polynomial approach to nonlinear time-delay systems,” In Ninth IFAC workshop on time-delay systems, Nantes, France, 2007.
[13]Q. Ma, “Some results on structural controllability of nonlinear systems,” Proceeding of 2010 International Conference on Intelligent Systems Design and Engineering Appilications (ISDEA2010), in press.
[14]Kaisheng Lu, Rational function systems and electric networks in multi-parameters. Beijing: Science press, 2010 (in Chinese).