State Observers and Unknown Input Estimators for Discrete-Time Nonlinear Systems Characterized by Incremental Multiplier Matrices

Novel discrete-time (DT) state observers and unknown input estimators are proposed for a class of DT nonlinear systems whose nonlinearity can be characterized by incremental multiplier matrices. The inputs to the nonlinear systems are allowed to have an unknown component. These nonlinear models are represented as linear models by treating the nonlinearity as a nonlinear input with a known structure. A novel DT state observer is proposed and a condition for its existence is given in terms of a linear matrix inequality (LMI). The unknown input estimator estimates the system unknown input with one sampling period time-delay. Unknown input estimators for continuous-time (CT) systems using their DT plant models are proposed. The proposed state observer and unknown input estimator are tested on numerical examples. An application of the proposed unknown input estimator to reconstruct malicious packet drops during the control signal transmission is given.