Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2012.18.6.513

Generalized Stability Condition for Descriptor Systems  

Oh, Do-Chang (Konyang University)
Lee, Dong-Gi (Konyang University)
Kim, Jong-Hae (Sunmoon University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.18, no.6, 2012 , pp. 513-518 More about this Journal
Abstract
In this paper, we propose a generalized index independent stability condition for a descriptor systemwithout any transformations of system matrices. First, the generalized Lyapunov equation with a specific right-handed matrix form is considered. Furthermore, the existence theorem and the necessary and sufficient conditions for asymptotically stable descriptor systems are presented. Finally, some suitable examples are used to show the validity of the proposed method.
Keywords
generalized Lyapunov equation; descriptor systems; index independent stability condition;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice Hall, Upper Saddle River, NJ, 1996.
2 W. Q. Liu and V. Sreeram, "Model reduction of singular systems," Proc. of the 39th IEEE Conference on Decision and Control, pp. 2373-2378, Sydney, Australia, 2000.
3 L. Zhang, J. Lam, and Q. Zhang, "Lyapunov and Riccati equations for discrete-time descriptor systems," IEEE Trans. Automat.Control, vol. 44, no. 11, pp. 2134-2139, 1999.   DOI
4 S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, PA, 1994.
5 A. Varga, "A descriptor systems toolbox for MATLAB," Proc. of the 2000 IEEE International Symposium on Computer Aided Control System Design, Anchorage, Alaska, pp. 25-27, Sep. 2000.
6 G. W. Stewart and J. G. Sun, Matrix Perturbation Theory, Academic Press, New York, 1990.
7 K. E. Chu, "The solution of the matrix equations AXB - CXD = E and (YA-DZ, YC-BZ) = (E, F)," Linear Algebra Appl., vol. 93, pp. 93-105, 1987.   DOI   ScienceOn
8 I. Masubuchi, Y. Kamitane, A. Ohara, and N. Suda, "$H{\infty}$ control for descriptor systems: a matrix inequalities approach," Automatica, vol. 33, no. 4, pp. 669-673, 1997.   DOI   ScienceOn
9 D. J. Bender, "Lyapunov-like equations and reachability/observability Gramians for descriptor systems," IEEE Transactions on Automatic Control, vol. 32, pp. 343-348, 1987.   DOI
10 J. Y. Ishihara and M. H. Terra, "On the Lyapunov theorem for singular systems," IEEE Transactions on Automatic Control, vol. 47, no. 11, pp. 1926-1930, 2002.   DOI
11 E. L. Yip and R. F. Sincovec, "Sovability, controllability and observability of continuous descriptor systems," IEEE Transactions on Automatic Control, vol. 26, pp. 702-707, 1981.   DOI
12 K. E. Brenan, S. L. Campbell, and L. R. Petzold, The Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations, Elsevier, North-Holland, NewYork, 1989.
13 P. J. Rabier and W. C. Rheinboldt, Nonholonomic Motion of Rigid Mechanical Systems from a DAE viewpoint, SIAM, Philadelphia, PA, 2000.
14 L. Dai, Singular Control Systems, Lecture Notes in Control and Information Sciences, 118, Springer-Verlag, Berlin, Heidelberg, 1989.
15 T. Penzl, "Numerical solution of generalized Lyapunovequations," Adv. Comput.Math., vol. 8, pp. 33-48, 1998.   DOI   ScienceOn
16 F. L. Lewis, "A tutorial on the geometric analysis of linear timeinvariant implicit systems," Automatica, vol. 28, pp. 119-137, 1992.   DOI
17 K. Takaba, N. Morihira, and T. Katayama, "A generalized Lyapunov theorem for descriptor system," Systems Control Lett., vol. 24, pp. 49-51, 1995.   DOI   ScienceOn
18 B. C. Moore, "Principal component analysis in linear systems: controllability, observability, and model reduction," IEEE Transactions on Automatic Control, vol. 26, pp. 17-32, 1981.   DOI
19 T. Stykel, "Solving projected generalized Lyapunov equations using SILICOT," IEEE International Symposium on Computer Aided Control System Design, Munich, Germany, 2006.
20 T. Stykel, "Analysis and numerical solution of generalized Lyapunov equations," Ph.D. Thesis, Institutfür Mathematik, Technische Universität Berlin, Germany, 2002.
21 D. C. Oh and D. G. Lee, "Stability analysis of descriptor system using generalized Lyapunov equation," Journal of IEEK, vol. 46SC, no. 4, pp. 49-62, 2009.   과학기술학회마을