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. Taylor, Adrien B.; Hendrickx, Julien M.; Glineur, François: Exact worst-case performance of first-order methods for composite convex optimization (2017)
  2. Ames, Brendan P.W.; Sendov, Hristo S.: Derivatives of compound matrix valued functions (2016)
  3. Daniilidis, Aris; Malick, Jerome; Sendov, Hristo: Spectral (isotropic) manifolds and their dimension (2016)
  4. Hilhorst, Gijs; Pipeleers, Goele; Michiels, Wim; Swevers, Jan: Sufficient LMI conditions for reduced-order multi-objective $\mathcal H_2/\mathcal H_\infty$ control of LTI systems (2015)
  5. Lee, Dong Hwan; Joo, Young Hoon; Tak, Myung Hwan: Periodically time-varying memory static output feedback control design for discrete-time LTI systems (2015)
  6. Wang, Shi; James, Matthew R.: Quantum feedback control of linear stochastic systems with feedback-loop time delays (2015)
  7. Luo, Ziyan; Tao, Jiyuan; Xiu, Naihua: Lowest-rank solutions of continuous and discrete Lyapunov equations over symmetric cone (2014)
  8. Rapisarda, P.; Rocha, P.: Lyapunov functions for time-relevant $2D$ systems, with application to first-orthant stable systems (2012)
  9. Henrion, Didier; Malick, Jér^ome: Projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions (2011)
  10. Shu, Zhan; Lam, James; Xiong, Junlin: Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach (2010)
  11. Xiong, Junlin; Ugrinovskii, Valery A.; Petersen, Ian R.: Decentralized output feedback guaranteed cost control of uncertain Markovian jump large-scale systems: local mode dependent control approach (2010)
  12. Lewis, A.S.; Luke, D.R.; Malick, J.: Local linear convergence for alternating and averaged nonconvex projections (2009)
  13. Menon, Prathyush P.; Edwards, Christopher: Decentralised static output feedback stabilisation and synchronisation of networks (2009)
  14. Nurdin, Hendra I.; James, Matthew R.; Petersen, Ian R.: Coherent quantum LQG control (2009)
  15. Subbotin, Maksim V.; Smith, Roy S.: Design of distributed decentralized estimators for formations with fixed and stochastic communication topologies (2009)
  16. Bianchi, Fernando D.; Mantz, Ricardo J.; Christiansen, Carlos F.: Multivariable PID control with set-point weighting via BMI optimisation (2008)
  17. Lewis, Adrian S.; Malick, Jér^ome: Alternating projections on manifolds (2008)
  18. Li, Li; Ugrinovskii, Valery A.; Orsi, Robert: Decentralized robust control of uncertain Markov jump parameter systems via output feedback (2007)
  19. Orsi, Robert; Helmke, Uwe; Moore, John B.: A Newton-like method for solving rank constrained linear matrix inequalities (2006)
  20. Yang, Kaiyang; Orsi, Robert: Generalized pole placement via static output feedback: a methodology based on projections (2006)