Observer design via interconnections of second-order mixed sliding-mode/linear differentiators

High-gain observers and sliding mode observers are two of the most common techniques to design observers (or differentiators) for lower triangular nonlinear dynamics. While sliding mode observers can handle globally bounded nonlinearities, high-gain linear techniques can deal with globally Lipschitz nonlinearities. To gain in generality and avoid the usual assumption that the plant's solutions are bounded with known bound, we propose here to mix both designs in the more general case where the nonlinearities satisfy a global incremental affine bound. We inspire from the recently developed low-power high-gain observer technique, which relies on the interconnection of several second-order high-gain observers. Adding sliding-mode correction terms into this low-power structure enables to guarantee global convergence of the estimation error in finite-time with gains depending only on the parameters of the incremental affine bound of the nonlinearities. The estimation error is also proved to be uniformly stable along solutions starting from any compact sets of initial conditions.