Impulsive observer-based design for state estimation of a class of nonlinear singularly perturbed systems with discrete measurements

Abstract

The state estimation problem of a class of nonlinear singularly perturbed systems with discrete measurements is investigated. The fast dynamics is assumed to be linear and exponentially stable. Under this assumption and some additional conditions, an asymptotic representation of the fast state is obtained in terms of the slow state and the known input. Then the full state estimation problem reduces to the slow state estimation problem. Based on this observation, an impulsive observer based estimation scheme is presented in the framework of singular perturbation. The continuous part of the proposed impulsive observer is a copy of the reduced-order slow dynamics of the observed system, while the impulse part is responsible for the implementation of the sample-triggered update of the observer state whenever a new sample of the output arrives. The estimation error is analyzed via a discontinuous Lyapunov function, and an ε-independent observer gain is designed. It is shown that the resulting estimation error exponentially converges towards an ultimate bound of order O(ε). The theoretical results are successfully applied to state estimates of Chua’s circuit and a flexible link robot. The simulation results demonstrate that the proposed state estimation scheme can achieve a desirable estimation accuracy for small enough ε>0.