Design of observers for non-linear time-varying systems

Novel stable observers are proposed for discrete, time-varying systems having time-varying, sector-bounded non-linearities. First, the form of the non-linearity is assumed to be known for all time and a stable non-linear filter is presented. Then assuming that the form of the non-linearity is not known but only a sector bound is given, we propose a linear filter and an upper bound on the sector constant to obtain a stable observer. The convergence conditions for the proposed observers are given directly in terms of the design parameters and are, therefore, very easy to check.