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

Z Q Ke, Hartmut Logemann, R Rebarber

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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.
Original languageEnglish
Pages (from-to)641-671
Number of pages31
JournalSIAM Journal on Control and Optimization
Issue number2
Early online date13 Feb 2009
Publication statusPublished - 2009



  • internal model principle
  • tracking
  • disturbance rejection
  • infinite-dimensional systems
  • discrete-time systems
  • sampled-data control
  • low-gain control

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