Parameterisation of a special class of saturated controllers and application to mechanical systems

This study provides a new parameterisation for a special class of nested‐saturation controllers, in which some multiplying coefficients appear before saturation functions. In an existing saturation scheme for the chain of integrators, the saturation levels and the multiplying coefficients are separately assigned in two stages, namely determined in the reduction analysis of saturated terms and the stability analysis of a reduced system. In the new parameterisation, it is in the saturation reduction analysis that the mentioned parameters are already determined. Such a convenient parameterisation is also applied to the uncertain multiple integrators and some mechanical systems.