Abstract
This paper considers the solution to a class of the second-order Sylvester matrix equation
This paper considers the solution to a class of the second-order Sylvester matrix equation
L. H. Keel, J. A. Fleming, and S. P. Bhattacharyya, “Minimum norm pole assignment via Sylvester's equation,” in Linear Algebra and Its Role in Systems Theory, vol. 47 of Contemporary Mathematics, pp. 265–272, American Mathematical Society, Providence, RI, USA, 1985.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. P. Bhattacharyya and E. de Souza, “Pole assignment via Sylvester's equation,” Systems & Control Letters, vol. 1, no. 4, pp. 261–263, 1982.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC.-C. Tsui, “A complete analytical solution to the equation and its applications,” IEEE Transactions on Automatic Control, vol. AC-32, no. 8, pp. 742–744, 1987.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG.-R. Duan, “Solution to matrix equation and eigenstructure assignment for descriptor systems,” Automatica, vol. 28, no. 3, pp. 639–642, 1992.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG.-R. Duan, “Solutions of the equation and their application to eigenstructure assignment in linear systems,” IEEE Transactions on Automatic Control, vol. AC-38, no. 2, pp. 276–280, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG.-R. Duan, “On the solution to the Sylvester matrix equation ,” IEEE Transactions on Automatic Control, vol. AC-41, no. 4, pp. 612–614, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetA. Saberi, A. A. Stoorvogel, and P. Sannuti, Control of Linear Systems with Regulation and Input Constraints, Communications and Control Engineering Series, Springer, London, UK, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetA. Jameson, “Solution of the equation by inversion of an or matrix,” SIAM Journal on Applied Mathematics, vol. 16, no. 5, pp. 1020–1023, 1968.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetE. de Souza and S. P. Bhattacharyya, “Controllability, observability and the solution of ,” Linear Algebra and Its Applications, vol. 39, pp. 167–188, 1981.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. E. Hartwig, “Resultants and the solution of ,” SIAM Journal on Applied Mathematics, vol. 23, no. 1, pp. 104–117, 1972.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Jones Jr. and C. Lew, “Solutions of the Lyapunov matrix equation ,” IEEE Transactions on Automatic Control, vol. AC-27, no. 2, pp. 464–466, 1982.
View at: Publisher Site | Google Scholar | MathSciNetJ. Z. Hearon, “Nonsingular solutions of ,” Linear Algebra and Its Applications, vol. 16, no. 1, pp. 57–63, 1977.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetV. Sreeram and P. Agathoklis, “Solution of Lyapunov equation with system matrix in companion form,” IEE Proceedings Control Theory and Applications D, vol. 138, no. 6, pp. 529–534, 1991.
View at: Google ScholarB. Zhou and G.-R. Duan, “An explicit solution to the matrix equation ,” Linear Algebra and Its Applications, vol. 402, pp. 345–366, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG.-R. Duan and G.-S. Wang, “Two analytical general solutions of the matrix equation ,” Journal of Harbin Institute of Technology, vol. 37, no. 1, pp. 1–4, 2005.
View at: Google Scholar | Zentralblatt MATH | MathSciNetG.-S. Wang and G.-R. Duan, “Robust pole assignment via P-D feedback in a class of second-order dynamic systems,” in Proceedings of the 8th International Conference on Control, Automation, Robotics and Vision (ICARCV '04), vol. 2, pp. 1152–1156, Kunming, China, December 2004.
View at: Publisher Site | Google ScholarG.-R. Duan and G.-S. Wang, “Eigenstructure assignment in a class of second-order descriptor linear systems: a complete parametric approach,” International Journal of Automation and Computing, vol. 2, no. 1, pp. 1–5, 2005.
View at: Publisher Site | Google ScholarG.-R. Duan and G.-P. Liu, “Complete parametric approach for eigenstructure assignment in a class of second-order linear systems,” Automatica, vol. 38, no. 4, pp. 725–729, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetG.-R. Duan, G.-S. Wang, and L. Huang, “Model reference control in second-order dynamic systems,” in Proceedings of the Control Conference (UKACC Control '04), Bath, UK, September 2004.
View at: Google ScholarG.-S. Wang, B. Liang, and G.-R. Duan, “Reconfiguring second-order dynamic systems via P-D feedback eigenstructure assignment: a parametric method,” International Journal of Control, Automation and Systems, vol. 3, no. 1, pp. 109–116, 2005.
View at: Google Scholar