This paper treats the systematic design of chaos generators which are capable of generating continuous-time signals with prescribed probability density function and power density spectra. For a specific signal model a statistical analysis is performed such that the inverse problem, i. e. the calculation of the model parameters from prescribed signal characteristics, can be solved. Finally from the obtained model parameters and the model structure the signal generating system is constructed. The approach is illustrated by several examples.

Discretely controlled continuous systems are characterised by their interacting continuous and discrete dynamics, where the continuous subsystem usually represents the system to be controlled and the discrete part describes the controller that switches the continuous system among different operation modes. This paper analyses systems where a perpetual switching of the operation mode has to occur in order to maintain the system's state in a prescribed operating region. It is shown how the analysis of the overall hybrid system can be simplified by using an embedded map that determines the behaviour at the switching instants.