## Abstract

Linear discrete-time systems with stochastic and deterministic polytopic type uncertainties in their state-space model are considered. A dynamic output-feedback controller is obtained via a new approach which allows a derivation of a controller in spite of parameter uncertainty. In the proposed approach the system is described via a difference equation and an augmented system is then used to obtain the output-feedback controller parameters. The controller is obtained without assuming a specific structure to the quadratic Lyapunov function and it is the first time that an output-feedback controller is obtained for robust state-multiplicative systems. The controller minimizes the stochastic l_{2}-gain of the closed-loop where a cost function is defined to be the expected value of the standard H_{∞} performance index with respect to the stochastic uncertainty. An example is given that demonstrates the merit of the theory.

Original language | English |
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Pages (from-to) | 3823-3828 |

Number of pages | 6 |

Journal | IFAC-PapersOnLine |

Volume | 50 |

Issue number | 1 |

DOIs | |

State | Published - Jul 2017 |

## Keywords

- Stochastic H output-feedback control
- multiplicative noise
- vertex-dependent Lyapunov function

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