# Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control

### Reference:

Ke, Z. Q., Logemann, H. and Rebarber, R., 2009. Approximate tracking and disturbance rejection for stable infinite-dimensional systems using sampled-data low-gain control. *SIAM Journal on Control and Optimization (SICON)*, 48 (2), pp. 641-671.

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### Official URL:

http://dx.doi.org/10.1137/080716517

### Abstract

In this paper we solve tracking and disturbance rejection problems for stable infinite-dimensional systems using a simple low-gain controller suggested by the internal model principle. For stable discrete-time systems, it is shown that the application of a low-gain controller ( depending on only one gain parameter) leads to a stable closed-loop system which asymptotically tracks reference signals r of the form r(k) = Sigma (N)(j=1) lambda(k)(j)tau(j), where tau(j) is an element of C and lambda(j) is an element of C with vertical bar lambda(j)vertical bar = 1 for j = 1, ... , N. The closed-loop system also rejects disturbance signals which are asymptotically of this form. The discrete-time result is used to derive results on approximate tracking and disturbance rejection for a large class of infinite-dimensional sampled-data feedback systems, with reference signals which are finite sums of sinusoids, and disturbance signals which are asymptotic to finite sums of sinusoids. The results are given for both input-output systems and state-space systems.

### Details

Item Type | Articles |

Creators | Ke, Z. Q., Logemann, H. and Rebarber, R. |

DOI | 10.1137/080716517 |

Uncontrolled Keywords | internal model principle, tracking, disturbance rejection, infinite-dimensional systems, discrete-time systems, sampled-data control, low-gain control |

Departments | Faculty of Science > Mathematical Sciences |

Publisher Statement | Logemann_SIAMJCO_2009_48_2_641.pdf: © 2009 Society for Industrial and Applied Mathematics |

Refereed | Yes |

Status | Published |

ID Code | 14298 |

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