Analysis of a multirate sampled-data implementation of a continuous-time, sliding-mode observer/controller pair

Abstract

An approach for closed-loop stability analysis of sampled-data implementations of control systems with Lipschitz-continuous non-linear elements is applied to a sliding-mode-based observer/controller pair. The stability analysis involves the evaluation of a finite horizon integral obtained from an L₂ -type analysis. This results in stability constraints involving matrix inequalities. The conditions raised can be satisfied for sufficiently fast sampling. The technique allows for incorporation of multiple sampling frequencies. Two sampling frequencies have been considered for the sliding-mode controller, a fast output sampling frequency and a slower controller sampling frequency. A numerical example illustrates some characteristics of the approach.

Acknowledgements

The authors acknowledge the support for G. Herrmann from the European Commission (TMR-grant, Project Number FMBICT983463).