Robust Nonlinear Observer for Lipschitz Nonlinear Systems Subject to Disturbances

Abstract

This note proposes a robust nonlinear observer for systems with Lipschitz nonlinearity. The proposed nonlinear observer, whose linear part adopts the linear LTR observer design technique, has two important advantages over previous designs. First, the new observer does not impose the small-Lipschitz-constant condition on the system nonlinearity, nor other structural conditions on the system dynamics as in the existing observer designs. Second, it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances.

Lyapunov stability analysis of second-order sliding-mode control and its application to chattering reduction design

“…Using (17), (20), and (21), one can show that the control law (21) drives the sliding surface σ such that it satisfies the second-order differential equation…”

“…In this paper, the proposed second-order sliding mode control is based on state feedback. It is mentioned that when the system state is not accessible, and only the system output is measured, one can use the robust observer proposed in [17] for accurate state estimation, and obtain an observer-based state feedback second-order sliding mode control. To confirm the effectiveness of the proposed chattering-free second-order sliding mode control design, two simulation examples are presented and compared.…”

State and Parameter Estimation for Nonlinear Delay Systems Using Sliding Mode Techniques

“…Like much of the existing work [4], [16], [2], it is required in this paper that the nonlinear terms satisfy the Lipschitz condition. From (11), in the new coordinates z, the bound ρ(·) defined in (3) can be expressed as ρ(t, z1(t), C…”

Coordinated control of multiple HVDC links using input–output exact linearization

“…If the rotor angles or speeds variables not are measurable an observer has to be used to estimate the variables [32,33].…”