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.

The conventional approach to reducing control signal chattering in sliding mode control is to use the boundary layer design. However, when there is high-level measurement noise, the boundary layer design becomes ineffective in chattering reduction. This paper, therefore, proposes a new design for chattering reduction by low-pass filtering the control signal. The new design is non-trivial since it requires estimation of the sliding variable via a disturbance estimator. The new sliding mode control has the same performance as the boundary layer design in noise-free environments, and outperforms the boundary layer design in noisy environments.

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This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disad-vantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t0). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.