### Abstract

We present the complete solution to the H^{∞}-optimal control problem when only sampled values of the state are available. For linear time-varying systems the optimum controller is characterized in terms of the solution of a particular generalized Riccati-differential equation, with the optimum performance determined by the conjugate point conditions associated with a family of generalized Riccati differential equations. For the infinite-horizon time-invariant problem, however, the optimum controller is characterized in terms of the solution of a particular generalized algebraic Riccati equation, and the performance is determined in terms of the conjugate-point conditions of a single generalized Riccati equation, defined on the longest sampling interval. If the distribution of the sampling times is also taken as part of the general design, uniform sampling turns out to be optimal for the infinite horizon case, while for the finite horizon problem a nonuniform sampling generally leads to a better performance.

Original language | English (US) |
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Pages (from-to) | 399-409 |

Number of pages | 11 |

Journal | Systems and Control Letters |

Volume | 16 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1991 |

### Keywords

- H-optimal control
- Riccati equations
- differential games
- sampled measurements

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)
- Mechanical Engineering
- Electrical and Electronic Engineering