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Zbl 0986.93072
Freiling, G.; Lee, S.-R.; Jank, G.
Coupled matrix Riccati equations in minimal cost variance control problems.
(English)
[J] IEEE Trans. Autom. Control 44, No.3, 556-560 (1999). ISSN 0018-9286

In the first part of the paper, the authors present an algorithm for the solution of a coupled system of algebraic matrix Riccati equation $$0= -A^T P- PA- Q+ PBR^{-1} B^T P- \gamma^2 VBR^{-1} B^T V,\tag 1$$ $$0= - A^T V- VA+ 2\gamma VBR^{-1} B^TV+ PBR^{-1} B^TV+ VBR^{-1} B^T P- 4PEWE^T P,\tag 2$$ where $P$ and $V$ are solutions of equations (1) and (2).\par The authors use the standard Lyapunov iteration approach and prove the convergence of the algorithm.\par In the second part of the paper, they derive sufficient conditions ensuring that the solutions of coupled matrix Riccati differential equations with the terminal values can not blow up on a given interval $[t_0, t_f]$.
[L.Socha (Katowice)]
MSC 2000:
*93E20 Optimal stochastic control (systems)
15A24 Matrix equations

Keywords: coupled Riccati equations; algebraic matrix Riccati equation; Lyapunov iteration approach; blow up

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