Robust Unknown Input Observer of Nonlinear Quadratic Systems With Application to Sensor Fault Estimation

Abstract

A robust unknown input observer (UIO) is designed for nonlinear quadratic systems (NQSs) affected by unknown input, disturbance, and noise. It is assumed that in this article the system states and their estimates are varying inside a hyper-rectangle region of known vertices. Based upon satisfying the observer matching condition and the minimum phase condition (at every vertex of the hyper-rectangle region of the system states and their estimates), a set of tractable linear matrix inequalities (LMIs) is derived for computing the design matrices of robust UIO. The design methodology of robust UIO is extended to NQSs affected by sensor fault, disturbance, and noise. By modeling the sensor fault as a system state with unknown sensor fault input, it is found that the observer matching condition is satisfied and only the minimum phase condition should be verified at every vertex of the hyper-rectangle region of the system states and their estimates. Another set of tractable LMIs is derived to compute the design matrices of robust UIO, which simultaneously estimates the system's states and sensor faults. A practical example of a nonlinear quadratic Rössler circuit affected by sensor fault, disturbance, and noise is used to show the design steps and to verify the proposed robust UIO. Simulation results indicate the ability of the proposed robust UIO to simultaneously estimate the system's states and sensor faults of NQSs affected by disturbance and noise.