We consider the numerical solution of large-scale continuous-time algebraic Riccati equations by Krylov subspace methods. We show that the solvability of the projected algebraic Riccati equation need not be assumed but can be inherited. This study of inheritance properties is the first of its kind. We conduct our study via the stabilizability and detectability of the control system, the stability of the associated Hamiltonian matrix and perturbation in terms of residuals. Special attention is paid to the stabilizing and positive semidefinite properties of approximate solutions. Illustrative numerical examples are presented.
|Effective start/end date
|2017/08/01 → 2018/07/31
- continuous-time algebraic Riccati equation
- Krylov subspace
- LQR optimal control
- projection method
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