Abstract:
A fast algorithm is proposed for checking the stability of the edges of a polytope where most of the computations involved depend on the number of vertices rather than on...Show MoreMetadata
First Page of the Article
Abstract:
A fast algorithm is proposed for checking the stability of the edges of a polytope where most of the computations involved depend on the number of vertices rather than on the number of edges. This algorithm is based on the segment lemma derived by H. Chapellat et al. (1988). Although the segment lemma is an important result on its own, no explicit algorithm was given there. Some important properties of the lemma are revealed, and it is shown how they lead to a fast algorithm. In this algorithm, the major computations involved are those of solving for the positive real roots of two polynomials with degree less than or equal to n/2 for each vertex. The computations required by the algorithm are mainly vertex-dependent, and the burden of the combinatoric explosion of the number of edges is greatly reduced.<>
Published in: IEEE Transactions on Automatic Control ( Volume: 35, Issue: 5, May 1990)
DOI: 10.1109/9.53530
First Page of the Article
Citations are not available for this document.
Cites in Papers - |
Cites in Papers - IEEE (6)
Select All
1.
M.S. Fadali, "Stability testing for systems with polynomial uncertainty", Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), vol.5, pp.3896-3901 vol.5, 2002.
2.
R.D. Kaminsky, T.E. Djaferis, "The finite inclusions theorem", Proceedings of 32nd IEEE Conference on Decision and Control, pp.508-518 vol.1, 1993.
3.
L.R. Pujara, N. Shanbhag, "Some stability theorems for polygons of polynomials", IEEE Transactions on Automatic Control, vol.37, no.11, pp.1845-1849, 1992.
4.
Y.Q. Shi, S.F. Zhou, "Stability of a set of multivariate complex polynomials with coefficients varying in diamond domain", IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.39, no.8, pp.683-688, 1992.
5.
L. R. Pujara, Naresh Shanbhag, "The Partition of Unstable Polygons of Polynomials", 1991 American Control Conference, pp.865-866, 1991.
6.
T. M. Murdock, W. E. Schmitendorf, S. Forrest, "Use of a Genetic Algorithm to Analyze Robust Stability Problems", 1991 American Control Conference, pp.886-889, 1991.
Cites in Papers - Other Publishers (13)
1.
Baltazar Aguirre-Hernandez, Raul Villafuerte-Segura, Alberto Luviano-Juarez, Carlos Arturo Loredo-Villalobos, Edgar Cristian Diaz-Gonzalez, "A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications", Complexity, vol.2020, pp.1, 2020.
2.
Baltazar Aguirre-Hernández, Faustino Ricardo García-Sosa, Carlos Arturo Loredo-Villalobos, Raúl Villafuerte-Segura, Eric Campos-Cantón, "Open Problems Related to the Hurwitz Stability of Polynomials Segments", Mathematical Problems in Engineering, vol.2018, pp.1, 2018.
3.
Marcelino Sánchez, Miguel Bernal, "A Convex Approach for Reducing Conservativeness of Kharitonov’s-Based Robustness Analysis", IFAC-PapersOnLine, vol.50, no.1, pp.832, 2017.
4.
Shih-Feng Yang, Chyi Hwang, "A test for robust Hurwitz stability of convex combinations of complex polynomials", Journal of the Franklin Institute, vol.339, no.2, pp.129, 2002.
5.
Chyi Hwang, Shih-Feng Yang, "The use of Routh array for testing the Hurwitz property of a segment of polynomials", Automatica, vol.37, no.2, pp.291, 2001.
6.
Shih-Feng Yang, Chyi Hwang, "Testing the robust Schur stability of a segment of complex polynomials", International Journal of Systems Science, vol.32, no.10, pp.1243, 2001.
7.
Chyi Hwang, Shih-feng Yang, "The Use of Routh Array for Testing the Hurwitz Property of a Segment of Polynomials", IFAC Proceedings Volumes, vol.33, no.13, pp.449, 2000.
8.
Jinsiang Shaw, Suhada Jayasuriya, "A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification", Journal of Dynamic Systems, Measurement, and Control, vol.118, no.3, pp.611, 1996.
9.
Gilles Ferreres, Jean-François Magni, "Robustness Analysis Using the Mapping Theorem without Frequency Gridding", IFAC Proceedings Volumes, vol.29, no.1, pp.3404, 1996.
10.
Marek K. Solak, "A structural approach to robust stability of polynomials", Multidimensional Systems and Signal Processing, vol.3, no.4, pp.421, 1992.
11.
F. J. KRAUS, W. TRUÖL, "Robust stability of control systems with polytopical uncertainty: a Nyquist approach", International Journal of Control, vol.53, no.4, pp.967, 1991.
12.
B. C. Chang, O. Ekdal, H. H. Yeh, S. S. Banda, "Computation of the real structured singular value via polytopic polynomials", Journal of Guidance, Control, and Dynamics, vol.14, no.1, pp.140, 1991.
13.
Marek K. Solak, "Convex combinations of G-stable polynomials", Multidimensional Systems and Signal Processing, vol.2, no.3, pp.337, 1991.
