Globally convergent real-time differentiation via second order sliding modes

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this article the design of a new real-time differentiator featuring global convergence properties is considered. Such a problem is tackled by means of a second-order sliding mode differentiator (2-SMD) with adjustable gain and switching logic. Due to its finite-time convergence and relaxed information demand regarding the signal to differentiate, the proposed differentiator appears well suited to be combined with output-feedback controllers. In order to point out the effectiveness and the convergence features of the proposed 2-SMD, some simulations related to a global output feedback stabilisation problem are presented.