## Abstract

We study constant input delay compensation by using finite-dimensional observer-based controllers in the case of the 1D heat equation. We consider Neumann actuation with nonlocal measurement and employ modal decomposition with $N+1$ modes in the observer. We introduce a chain of $M$ sub-predictors that leads to a closed-loop ODE system coupled with infinite-dimensional tail. Given an input delay $r$ , we present LMI stability conditions for finding $M$ and $N$ and the resulting exponential decay rate and prove that the LMIs are always feasible for any $r$. We also consider a classical observer-based predictor and show that the corresponding LMI stability conditions are feasible for any $r$ provided $N$ is large enough. A numerical example demonstrates that the classical predictor leads to a lower-dimensional observer. However, it is known to be hard for implementation due to the distributed input signal.

Original language | English |
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Article number | 9442823 |

Pages (from-to) | 626-631 |

Number of pages | 6 |

Journal | IEEE Control Systems Letters |

Volume | 6 |

DOIs | |

State | Published - 2022 |

## Keywords

- Distributed parameter systems
- observer-based control
- time-delay