Discrete valued feedback laws and the Zeno phenomenon

We consider closed loop control systems in which feedback laws take values in a discrete set U and we study the Zeno phenomenon, i.e. the accumulation of discontinuities with respect to time. The results generalize those obtained in [F. Ceragioli, Finite valued feedback laws and piecewise classical solutions, Nonlinear Analysis 65 (2006) 984-998] for the case where U is finite to the case where U may be infinite. An application to a quantized control problem is also shown.