Reduced-order dynamic observer error linearisation for discrete-time systems: an extension of the classical observer error linearisation

This study addresses reduced-order dynamic observer error linearisation (RDOEL) for discrete-time systems, which is a modified version of dynamic observer error linearisation (DOEL). The authors define the concept of RDOEL and provide a necessary and sufficient condition for RDOEL. Moreover, the relation between RDOEL and DOEL is discussed when the auxiliary dynamics is an arbitrary linear controllable system. Using the relationship and an existing algorithm for DOEL, an algorithm for RDOEL also proposed, which offers lower-dimensional observers than DOEL. Finally, the authors illustrate the theory by applying it to the discrete-time hyperchaotic system due to Wang, which was derived from the generalised Rössler system via a first-order difference algorithm.