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Adaptive stabilization using a variable sampling rate. (English) Zbl 0845.93074
Consider an adaptive stabilization problem for a single-input single-output linear minimum phase system (1) \(\begin{cases} \dot x = Ax + Bu \\ y = Cx. \end{cases}\) such that \(CB > 0\), by means of the feedback law (2) \(u = - ky\), \(\dot k = y^2\). It is known that, when the feedback is implemented digitally, for particular choices of the initial values \(x_0\), \(k_0\) and of the (constant) sampling rate \(h\), the computed solution may diverge, in contrast with the prediction of the continuous time theoretical results. To face this problem the author considers variable sampling rates and a discrete analog of (2). The control gain depends on the current sampling rate at each step. Stabilization is achieved in such a way that the sequence of measured outputs tends to zero. Results are provided for both cases where the sign of CB is known or not known.

MSC:
93D21 Adaptive or robust stabilization
93C57 Sampled-data control/observation systems
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