Ziyan Luo

Lowest-rank Solutions of Continuous and Discrete Lyapunov Equations over Symmetric Cone

  • Ziyan Luo
  • Jiyuan Tao
  • Naihua Xiu
    • Categories Control Applications, Linear, Cone and Semidefinite Programming Tags , , , ,

    The low-rank solutions of continuous and discrete Lyapunov equations are of great importance but generally difficult to achieve in control system analysis and design. Fortunately, Mesbahi and Papavassilopoulos [On the rank minimization problems over a positive semidefinite linear matrix inequality, IEEE Trans. Auto. Control, Vol. 42, No. 2 (1997), 239-243] showed that with the semidefinite … Read more

    The Nonnegative $ Norm Minimization under Generalized hBcmatrix Measurement

  • Lingchen Kong
  • Ziyan Luo
  • Linxia Qin
  • Naihua Xiu
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper, we consider the $l_0$ norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized $Z$-matrix for a rectangular matrix, we show that this $l_0$ norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the corresponding $l_p$ ($0