## Abstract

The linear-quadratic (LQ) control problem is considered for a class of infinite-dimensional systems with bounded input and output operators, that are not exponentially stabilizable, but only strongly stabilizable. A sufficient condition for the existence of a minimizing control and of a stabilizing solution to the associated LQ Riccati equation is given. The main contribution of this paper is the convergence of the stabilizing solutions of a sequence of finite-dimensional Riccati equations to the strongly stabilizing solution of the infinite-dimensional Riccati equation. The result is applied to a model of propagation of sound waves in a one-dimensional wave-guide.

Original language | English |
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Pages (from-to) | 1909-1937 |

Number of pages | 29 |

Journal | SIAM Journal on Control and Optimization |

Volume | 38 |

Issue number | 6 |

Publication status | Published - 4-Aug-2000 |

## Keywords

- linear quadratic control problem
- algebraic Riccati equation on Hilbert space
- dissipative systems
- collocated actuators and sensors
- QUADRATIC OPTIMAL-CONTROL
- LINEAR-SYSTEMS