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**Stability and limit oscillations of a control event-based sampling criterion.**
*(English)*
Zbl 1244.93131

Summary: This paper investigates the presence of limit oscillations in an adaptive sampling system. The basic sampling criterion operates in the sense that each next sampling occurs when the absolute difference of the signal amplitude with respect to its currently sampled signal equalizes a prescribed threshold amplitude. The sampling criterion is extended involving a prescribed set of amplitudes. The limit oscillations might be interpreted through the equivalence of the adaptive sampling and hold device with a nonlinear one consisting of a relay with multiple hysteresis whose parameterization is, in general, dependent on the initial conditions of the dynamic system. The performed study is performed on the time domain.

### MSC:

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

34C25 | Periodic solutions to ordinary differential equations |

94A20 | Sampling theory in information and communication theory |

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\textit{M. de La Sen} et al., J. Appl. Math. 2012, Article ID 684292, 25 p. (2012; Zbl 1244.93131)

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### References:

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