Matrix Riccati Equations in Control and Systems Theory

By H. Abou-Kandil, Gerhard Freiling, V. Ionescu, G. Jank. IEEE Transactions on Automatic Control, 2003

680 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/5ce32a7eba2f78cf8398a534357d36aae2ab311b

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Citations in the corpus

Optimal investment-consumption-insurance with random parameters (2016, positive): “By Radon’s lemma (see Abou-Kandil et al. 2003 or Chiu & Wong 2011), however, the solution of M1 can be represented explicitly in terms of a solvable linear matrix-valued ODE as follows: M1( ) = M1(t, s) = R2( )R1( )−1, := s − t, (66) where R1( ), R2( ) ∈ C(T ; n×n) and R( ) := (R1( ) , R2( ) ) is…”
Portfolios and risk premia for the long run. (2012, neutral): “It does not admit a closed-form solution in terms of matrix operations but numerical techniques for obtaining the solution are available [see Abou-Kandil et al. (2003), Chapter 2]. Once the matrix v1 is known, the linear equation (55) yields a unique solution for v0 and λ is quadratic in v0 and line”
AN EXTENDED BLOCK ARNOLDI ALGORITHM FOR LARGE-SCALE SOLUTIONS OF THE CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATI ON ∗ (2008, background): “on the unit square [0, 1] × [0, 1] with homogeneous Dirichlet boundary conditions.”
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations (2006, background): “See [1], [7], [23], [30] for detailed coverage of Hamiltonian and symplectic matrices, and [12], [28] for properties of matrices in the Lie algebra or Lie group of more general scalar products.”
Dependent Risk Models with Bivariate Phase-Type Distributions (2009, methodology): “When the fluid level decreases at rate c and the process Z is in some states in E1, the process J∗ would enter S0 upon transition of Z into Γ2 which could happen through (1) transition into E2 (governed by T12), or (2) transition into ∆ (governed by t1).”