Minimal-norm static feedbacks using dissipative Hamiltonian matrices
Publication date :
01 August 2021
Journal title :
Linear Algebra and its Applications
ISSN :
0024-3795
eISSN :
1873-1856
Publisher :
Elsevier, Netherlands
Volume :
623
Pages :
258-281
Peer reviewed :
Peer Reviewed verified by ORBi
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R450 - Institut NUMEDIART pour les Technologies des Arts Numériques
Albert, A., Conditions for positive and nonnegative definiteness in terms of pseudoinverses. SIAM J. Appl. Math. 17:2 (1969), 434–440.
Anderson, B., Bose, N., Jury, E., Output feedback stabilization and related problems – solution via decision methods. IEEE Trans. Autom. Control 20:1 (1975), 53–66.
Arzelier, D., Deaconu, G., Gumussoy, S., Henrion, D., H2 for HIFOO. International Conference on Control and Optimization with Industrial Applications, 2011, Bilkent University, Ankara, Turkey.
Åström, K.J., Murray, R.M., Feedback Systems: An Introduction for Scientists and Engineers. 2010, Princeton University Press.
Blondel, V., Tsitsiklis, J., NP-hardness of some linear control design problems. SIAM J. Control Optim. 35:6 (1997), 2118–2127.
Choudhary, N., Gillis, N., Sharma, P., On approximating the nearest Ω-stable matrix. Numerical Linear Algebra with Applications, 2019, 10.1002/nla.2282.
Gillis, N., Sharma, P., On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Automatica 85 (2017), 113–121.
Gillis, N., Sharma, P., Finding the nearest positive-real system. SIAM J. Numer. Anal. 56:2 (2018), 1022–1047.
Grant, M., Boyd, S., Graph implementations for nonsmooth convex programs. Recent Advances in Learning and Control, 2008, 95–110.
Grippo, L., Sciandrone, M., On the convergence of the block nonlinear Gauss–Seidel method under convex constraints. Oper. Res. Lett. 26:3 (2000), 127–136.
Gumussoy, S., Henrion, D., Millstone, M., Overton, M.L., Multiobjective robust control with HIFOO 2.0. IFAC Proc. Vol. 42:6 (2009), 144–149.
Henrion, D., Lofberg, J., Kocvara, M., Stingl, M., Solving polynomial static output feedback problems with PENBMI. Proceedings of the 44th IEEE Conference on Decision and Control, 2005, 7581–7586.
Iwasaki, T., Skelton, R., All controllers for the general H∞ control problem: LMI existence conditions and state space formulas. Automatica 30:8 (1994), 1307–1317.
Iwasaki, T., Skelton, R., Geromel, J., Linear quadratic suboptimal control with static output feedback. Syst. Control Lett. 23:6 (1994), 421–430.
Leibfritz, F., Compleib, constraint matrix-optimization problem library-a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Dept. Math., 2004, Univ. Trier, Trier, Germany Tech. Rep.
Mehl, C., Mehrmann, C., Sharma, P., Stability radii for linear Hamiltonian systems with dissipation under structure-preserving perturbations. SIAM J. Matrix Anal. Appl. 37:4 (2016), 1625–1654.
Mesbahi, M., A semi-definite programming solution of the least order dynamic output feedback synthesis problem. Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No. 99CH36304), vol. 2, 1999, 1851–1856.
Nemirovskii, A., Several NP-hard problems arising in robust stability analysis. Math. Control Signals Syst. 6:2 (1993), 99–105.
Peretz, Y., A characterization of all the static stabilizing controllers for LTI systems. Linear Algebra Appl. 437:2 (2012), 525–548.
Peretz, Y., A randomized approximation algorithm for the minimal-norm static-output-feedback problem. Automatica 63 (2016), 221–234.
Polyak, B., Khlebnikov, M., Shcherbakov, P., An LMI approach to structured sparse feedback design in linear control systems. 2013 European Control Conference (ECC), 2013, 833–838.
Spencer, B.F., Sain, M.K., Controlling buildings: a new frontier in feedback. IEEE Control Syst. 17:6 (1997), 19–35.
Sun, J.G., Backward perturbation analysis of certain characteristic subspaces. Numer. Math. 65 (1993), 357–382.
Syrmos, V.L., Abdallah, C.T., Dorato, P., Grigoriadis, K., Static output feedback: a survey. Automatica 33:2 (1997), 125–137.
Toh, K.C., Todd, M., Tütüncü, R., SDPT3–a MATLAB software package for semidefinite programming, version 1.3. Optim. Methods Softw. 11:1–4 (1999), 545–581.
Trentelman, H.L., Stoorvogel, A.A., Hautus, M., Control Theory for Linear Systems. 2012, Springer Science & Business Media.
Tütüncü, R., Toh, K., Todd, M., Solving semidefinite-quadratic-linear programs using SDPT3. Math. Program. 95:2 (2003), 189–217.
Xu, Y., Teng, J., Optimum design of active/passive control devices for tall buildings under earthquake excitation. Struct. Des. Tall Spec. Build. 11:2 (2002), 109–127.
Yang, J.N., Lin, S., Jabbari, F., H2-based control strategies for civil engineering structures. J. Struct. Control. 10:3–4 (2003), 205–230.