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Hurwitz-Schur Stability Test of 2-D Polynomials

version (2.13 KB) by Yang Xiao
This program can test the Hurwitz-Schur Stability of 2-D Polynomials.


Updated 08 Aug 2007

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Hurwitz-Schur Stability Test of 2-D Polynomials

Copyright (C) Yang XIAO, Beijing Jiaotong University, Aug.8, 2007, E-Mail:

The stability of 2-D continuous-discrete systems and time-delay systems can be determined by the Hurwitz-Schur Stability of characteristic polynomials of the systems [1-3].
The characteristic polynomials can be expressed as a 2-D Polynomial in s-z domain: B(z1,z2)=[1 z^(-1) z^(-2)]*B*[1 s s^2]'.
This program derived from the main results of Ref. [1-3], and it can test the Hurwitz-Schur Stability of 2-D Polynomials.

[1] Y. Xiao; Stability test for 2-D continuous-discrete systems, Proceedings of the 40th IEEE Conference on Decision and Control, 2001. Volume 4,4-7 Dec. 2001
Page(s):3649 - 3654 vol.4
[2] Y. Xiao Yang, 2-D stability test for time-delay systems, Proceedings of 2001 International Conferences on Info-tech and Info-net, 2001. ICII 2001 - Beijing. Volume 4, 29 Oct.-1 Nov. 2001 Page(s):203 - 208 vol.4
[3] Y. Xiao; 2-D algebraic test for stability of time-delay systems, Proceedings of the 2002 American Control Conference, 2002. Volume 4, 8-10 May 2002 Page(s):3351 - 3356 vol.4
[4] Y. Xiao, Stability Analysis of Multidimensional Systems, Shanghai Science and Technology Press, Shanghai, 2003.
The papers [1-3] can be downloaded from Web site of IEEE Explore.

Comments and Ratings (1)


Dear Yang Xiao

I perused your Hurwitz-Schur stability test with matlab program algorithm and run-times.

[1]. If you use the matlab-vector application instead of for-next(end) procedure than it is more speedly.
For example:


[2] If you make this m-file, one matlab sub-function than be very usefully for users.

Good works, best regards

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux

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