Observer design for generalized sector-bounded noisy nonlinear systems

Abstract

This article presents a new observer for a class of nonlinear systems, defined as a “generalized sector-bounded” nonlinear system, in the presence of both sensor and input disturbances. The generalized sector-bounded nonlinearity is shown to be a super-set of Lipschitz, bounded Jacobian, one-sided Lipschitz, monotonically increasing and dissipative nonlinearities. This article presents necessary and sufficient conditions for this observer to guarantee a desired minimum performance. The conditions for the observer are presented as a linear matrix inequality that can be solved offline using commercial solvers, and the solution to the linear matrix inequality is used to explicitly compute the observer gain. This article then extends these results to case where an additive nonlinearity appears in the sensor output. The use of the methodology developed in this article is demonstrated through illustrative examples. Compared to previous results on nonlinear observers, the proposed observer guarantees a global performance measure for a very general class of nonlinear systems and does not require online computation of the observer gain.