### Reference:

Opmeer, M. R. and Staffans, O. J., 2010. Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection. *SIAM Journal on Control and Optimization (SICON)*, 48 (8), pp. 5084-5107.

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### Abstract

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in general, unbounded and even nondensely defined). We further show that after renorming the state space in terms of the inverse of the smallest solution of the filter Riccati equation, the closed-loop system is not only input-output stable but also strongly internally *-stable.

Item Type | Articles |

Creators | Opmeer, M. R.and Staffans, O. J. |

DOI | 10.1137/090762233 |

Related URLs | |

Uncontrolled Keywords | infinite-dimensional system,input-output stabilization,linear quadratic optimal control,riccati equation,left factorization,output injection |

Departments | Faculty of Science > Mathematical Sciences |

Publisher Statement | Opmeer_SICON_2010_48_8_5084.pdf: © 2010 Society for Industrial and Applied Mathematics |

Refereed | Yes |

Status | Published |

ID Code | 22890 |

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