µ-Values for Matrices Corresponding to Symmetries in Control Systems
Main Article Content
Abstract
In this article we consider numerical approximation of structured singular values ($\mu-$values). The lower bounds for $\mu-$values are approximated by using ordinary differential equations based technique. The structured singular values provide a vital tool to investigate stability of feedback systems. We also compute the lower bounds of $\mu-$values for certain matrices that correspond to symmetries in control systems.
Article Details
References
- Bernhardsson, Bo and Rantzer, Anders and Qiu, Li. Real perturbation values and real quadratic forms in a complex vector space. Linear Algebra Appl., 1(1994): 131-154.
- Braatz, Richard P and Young, Peter M and Doyle, John C and Morari, Manfred. Computational complexity of µ calcu- lation. IEEE Trans. Autom. Control, 39(1994): 1000-1002.
- Chen, Jie and Fan, Michael KH and Nett, Carl N. Structured singular values with nondiagonal structures. I. Characteri- zations. IEEE Trans. Autom. Control, 41(1996): 1507-1511.
- Danielson, Claus Robert. Symmetric constrained optimal control: Theory, algorithms, and applications. University of California, Berkeley, 2014.
- Fan, Michael KH and Tits, André L and Doyle, John C. Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Trans. Autom. Control, 36(1991): 25-38
- Hinrichsen, D and Pritchard, AJ. Mathematical systems theory I, vol. 48 of Texts in Applied Mathematics. Springer- Verlag, Berlin Volume 48(2005).
- Karow, Michael and Kokiopoulou, Effrosyni and Kressner, Daniel. On the computation of structured singular values and pseudospectra. Syst. Control Lett. 59(2010): 122-129.
- Karow, Michael and Kressner, Daniel and Tisseur, Fran ¸coise. Structured eigenvalue condition numbers. SIAM J. Matrix Anal. Appl. 28(2006): 1052-1068.
- Packard, Andrew and Doyle, John. The complex structured singular value. Automatica 29(1993): 71-109.
- Packard, Andy and Fan, Michael KH and Doyle, John. A power method for the structured singular value. Decision and Control, 1988., Proceedings of the 27th IEEE Conference on, 2132-2137, (1998).
- Qiu, Li and Bernhardsson, Bo and Rantzer, Anders and Davison, EJ and Young, PM and Doyle, JC. A formula for computation of the real stability radius. Automatica, 31(1995), 879-890.
- Rehman, Mutti-Ur and Tabassum, Shabana Numerical Computation of Structured Singular Values for Companion Ma- trices. J. Appl. Math. Phys., 5(2017), 1057-1072.
- Doyle, John Analysis of feedback systems with structured uncertainties. IEEE Proc. D-Control Theory Appl., 129(1982), 242-250.
- Ferreres, Gilles A practical approach to robustness analysis with aeronautical applications. Springer Science & Business Media, (1999)
- Fu, Minyue The real structured singular value is hardly approximable. IEEE Trans. Autom. Control, 42(1997), 1286 - 1288.
- Newlin, Matthew P and Glavaski, Sonja T Advances in the computation of the/spl mu/lower bound. Proc. 1995 Amer. Control Conf., (1995).