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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