References
- Balakrishnan, V. , & Vandenberghe, L. (2003). Semidefinite programming duality and linear time-invariant systems. IEEE Transactions on Automatic Control, 48 (1), 30–41.
- Borwein, M. J. , & Wolkowicz, H. (1981). Facial reduction for a cone-convex programming problem. Journal of the Australian Mathematical Society, 30 , 369–380.
- de Klerk, E. (2002). Aspects of semidefinite programming . Dordrecht: Netherlands: Kluwer Academic.
- Ebihara, Y. , (2012). Systems control using LMI (in Japanese) . Tokyo: Japan: Morikita Publishing.
- Freund, R. M. , Ordóñez, F. , & Toh, K. C. (2007). Behavioral measures and their correlation with IPM iteration counts on semi-definite programming problems. Mathematical Programming, 109 , 445–475.
- Gärtner, B. , , & Matoušek, J. (2012). Approximation algorithms and semidefinite programming . Berlin: Germany: Springer.
- Henrion, D. , & Lasserre, J. B. (2005). Detecting global optimality and extracting solutions in GloptiPoly, In D. Henrion & A. Garulli (Eds.), Positive polynomials in control. Berlin: Germany: Springer.
- Iwasaki, T. , & Skelton, R. E. (1994). All controllers for the general H ∞ control problem: LMI existence conditions and state space formulas. Automatica, 30 , 1307–1317.
- Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of 2004 IEEEE International Symbosium on Computer Aided COntrol SYstems Design, New Orleans, USA.
- Mittelmann, D. H. (2003). An independent benchmarking of SDP and SOCP solvers. Mathematical Programming, 95 , 407–430.
- Navascués, M. , García-Sáez, A. , Acín, A. , Pironio, S. , & Plenio, M. B. (2013). A paradox in bosonic energy computations via semidefinite programming relaxations. New Journal of Physics, 15 , doi: 10.1088/1367-2630/15/2/023026.
- Pataki, G. (2013). Springer proceedings in mathematics & statistics strong duality in conic linear programming: Facial reduction and extended dual (Vol. 50, pp. 613–634) . New York, NY: Springer.
- Ramana, M. V. (1997). An exact duality theory for semidefinite programming and its complexity implications. Mathematical Programming, 77 , 129–162.
- Ramana, M. V. , Tunçel, L. , & Wolkowicz, H. (1997). Strong duality for semidefinite programming. SIAM Journal on Optimization, 7 (3), 641–662.
- Renegar, J. (2001). A mathematical view of interior-point methods in convex optimization . Philadelphia: USA: SIAM.
- Scherer, C. (1992a). H ∞-control by state feedback for plants with zeros on the imaginary axis. SIAM Journal on Control and Optimization, 30 (1), 123–142.
- Scherer, C. (1992b). H ∞-optimization without assumptions on finite or infinite zeros. SIAM Journal on Control and Optimization, 30 (1), 143–166.
- Sekiguchi, Y. , & Waki, H. (2016). Perturbation analysis of singular semidefinite program and its application to a control problem, Retreived from Arxiv : https://arxiv.org/abs/1607.05568.
- Silverman, L. M. (1969). Inversion of multivariable linear systems. IEEE Transactions on Automatic Control, AC-14 (3), 270–276.
- Stoorvogel, A. A. (1991). The singular H ∞ control problem with dynamic measurement feedback. SIAM Journal on Control and Optimization, 29 (1), 160–184.
- Sturm, J. F. (1999). Using SeDuMi 1.02, a Matlab toolbox for optimization over symmetric cones. Optimization Methods and Software, 11 , 625–653.
- Toh, K. C. , Todd, M. , & Tütüncü, R. H. (1999). SDPT3 – a Matlab software package for semidefinite programming. Optimization Methods and Software, 11 , 545–581.
- Trnovská, M. (2005). Strong duality conditions in semidefinite programming. Journal of Electrical Engineering, 6 , 1–5.
- Vandenberghe, L. , Balakrishnan, V. , Wallin, R. , Hansson, A. , & Roh, T. (2005). Interior-point algorithms for semidefinite programming problems derived from the KYP lemma. In D. Henrion & A. Garulli (Eds.), Positive polynomials in control . Berlin: Germany: Springer.
- Waki, H. , & Muramatsu, M. (2013). Facial reduction algorithms for conic optimization problems. Journal of Optimization Theory and Applications, 158 , 188–215.
- Waki, H. , & Sebe, N. (2015). Application of facial reduction to H ∞ state feedback control problem. In Proceedings of the 8th IFAC robust control design (ROCOND 2015) (pp. 112–118). Bratislava, Slovak Republic.
- Yamashita, M. , Fujisawa, K. , & Kojima, M. (2003). Implementation and evaluation of SDPA 6.0 (SemiDefinite Programming Algorithm 6.0). Optimization Methods and Software, 18 , 491–505.