H filter design for a class of nonlinear discrete-time singular systems

This paper deals with the H filter design problem for a class of discrete-time Lipschitz nonlinear singular systems. The approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors. Sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given. The method also unifies the design for the full-order, reduced-order, minimal-order filters for discrete- time systems. The presented results are less conservative than those existing in the literature, this is due to the introduction of new slack variables. Application to systems with unknown input is presented via a numerical example.