Nonlinear filtering design for discrete-time systems using sliding window of delayed measurements
Abstract
This chapter focuses on the observer design for a class of Lipschitz discrete-time systems with bounded disturbances. The objective of this chapter is to develop a novel and simple observer design method so that wider ranges of problems can be solved without too much of mathematics overhead. The main idea consists in using sliding window of delayed measurements in a Luenberger structure observer in order to get nonrestrictive sufficient conditions. The presented results are in the form of bilinear matrix inequality (BMI) transformed to a convex problem (linear matrix inequality-LMI) through a useful approach. The resulting constraint can be easily achieved with standard software algorithms. To prove the superiority of the proposed approach, a comparison with the classical case is presented. Simulation results are given to illustrate the effectiveness and the high performances of the sliding window filter.