LMI-based sliding-mode observer design method

In an LMI-based sliding-mode observer design method for a class of multivariable uncertain systems the switching surface is set to be the difference between the observer and system output. In terms of LMIs, a necessary and sufficient condition is derived for the existence of a sliding-mode observer guaranteeing a stable sliding motion on the switching surface that is insensitive to matched uncertainties. The gain matrices of the sliding-mode observer are characterised using the solution of the LMI existence condition. The approach is direct and does not require state transformation, and has advantages in computation.