The linear matrix inequality (LMI) problem is a well known type of convex feasibility problem that has found many applications to controller analysis and design. The rank constrained LMI problem is a natural as well as important generalization of this problem. It is a nonconvex feasibility problem de¯ned by LMI constraints together with an additional matrix rank constraint. Interest in rank constrained LMIs arises as many important output feedback and robust control problems, that cannot always be addressed in the standard LMI framework, can be formulated as special cases of this problem [10], [37], [16], [30]. Examples include bilinear matrix inequality (BMI) problems, see [16] and [30], that are easily seen to be equivalent to rank one constrained LMI problems.

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  1. Uschmajew, André; Vandereycken, Bart: Geometric methods on low-rank matrix and tensor manifolds (2020)
  2. Xiang, Chengdi; Petersen, Ian R.; Dong, Daoyi: Static and dynamic coherent robust control for a class of uncertain quantum systems (2020)
  3. Lee, Donghwan; Hu, Jianghai: Sequential parametric convex approximation algorithm for bilinear matrix inequality problem (2019)
  4. Wang, Yan; Rajamani, Rajesh; Zemouche, Ali: A quadratic matrix inequality based PID controller design for LPV systems (2019)
  5. Mousavi, Mehdi S.; Sendov, Hristo S.: A unified approach to spectral and isotropic functions (2018)
  6. Naldi, Simone: Solving rank-constrained semidefinite programs in exact arithmetic (2018)
  7. Wang, Yan; Zemouche, Ali; Rajamani, Rajesh: A sequential LMI approach to design a BMI-based multi-objective nonlinear observer (2018)
  8. Sun, Chuangchuang; Dai, Ran: Rank-constrained optimization and its applications (2017)
  9. Taylor, Adrien B.; Hendrickx, Julien M.; Glineur, François: Exact worst-case performance of first-order methods for composite convex optimization (2017)
  10. Wang, Shi; Gao, Qing; Dong, Daoyi: Robust (H^\infty) controller design for a class of linear quantum systems with time delay (2017)
  11. Yang, Hongli; Zhao, Maoxian: An augmented Lagrangian method for the optimal (H_\infty) model order reduction problem (2017)
  12. Ames, Brendan P. W.; Sendov, Hristo S.: Derivatives of compound matrix valued functions (2016)
  13. Daniilidis, Aris; Malick, Jerome; Sendov, Hristo: Spectral (isotropic) manifolds and their dimension (2016)
  14. Hilhorst, Gijs; Pipeleers, Goele; Michiels, Wim; Swevers, Jan: Sufficient LMI conditions for reduced-order multi-objective (\mathcalH_2/\mathcalH_\infty) control of LTI systems (2015)
  15. Kovalsky, S. Z.; Glasner, D.; Basri, R.: A global approach for solving edge-matching puzzles (2015)
  16. Lee, Dong Hwan; Joo, Young Hoon; Tak, Myung Hwan: Periodically time-varying memory static output feedback control design for discrete-time LTI systems (2015)
  17. Wang, Shi; James, Matthew R.: Quantum feedback control of linear stochastic systems with feedback-loop time delays (2015)
  18. Harno, Hendra G.; Petersen, Ian R.: Robust (H^\infty) control via a stable decentralized nonlinear output feedback controller (2014)
  19. Harno, Hendra G.; Petersen, Ian R.: Decentralized state feedback robust (H^\infty) control using a differential evolution algorithm (2014)
  20. Luo, Ziyan; Tao, Jiyuan; Xiu, Naihua: Lowest-rank solutions of continuous and discrete Lyapunov equations over symmetric cone (2014)

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