Left invertibility of piecewise smooth system: The Alpazur case

The paper deals with left invertibility problem for nonsmooth systems, the illustrative case is a data secure transmission, but this problem occurs also in fault detection, parameters estimation and control design from a desired output behaviour. Here the left invertibility problem is treated on the basis of a nonsmooth chaotic system, the well known Alpazur circuit. It is associated to its dynamic input (the message). Two possibilities of implementing such a data secure transmission are given and treated independently, taking into account the particularities of each one. A high order sliding mode observer is used in one scenario, while a step-by-step observer is implemented in the other. Detailed simulation information is presented in order to emphasize the premises stated at the beginning.