## Abstract

In this paper we consider time{varying linear systems on Hilbert spaces and study the optimal control problem with indefinite performance criteria over a finite horizon interval. Due to the indefiniteness of the cost function, the associated integral Riccati equation in general does not process a solution on the whole interval. Applying an operator theoretic approach due to Hinrichsen and Pritchard [10] equivalent conditions are arrived for the unique solvability of the linear quadratic optimization problem and for the existence of solutions to the integral Riccati equation. Contrary to the finite

dimensional situation these problems are not generally equivalent. The results are applied to a parameterized Riccati equation which plays an important role in robustness analysis.

dimensional situation these problems are not generally equivalent. The results are applied to a parameterized Riccati equation which plays an important role in robustness analysis.

Original language | English |
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Number of pages | 28 |

Journal | Journal of mathematical systems, estimation and control |

Volume | 5 |

Issue number | 1 |

Publication status | Published - 1995 |

Externally published | Yes |