Super twisting algorithm-based step-by-step sliding mode observers for nonlinear systems with unknown inputs

Abstract

. Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputs. International Journal of Systems Science, Taylor Francis, 2007, 38 (10), pp.803-815. inria-00128137v2 Super twisting algorithm based step-by-step sliding mode observers for nonlinear systems with unknown inputsThis paper highlights the interest of step-by-step higher order sliding mode observers for MIMO nonlinear systems with unknown inputs. A structural matching condition, stating on the possibility to design such observers and to reconstruct the unknown inputs, is derived. A finite time sliding mode observer, based on the hierarchical use of the super twisting algorithm, is developed. Then, it is shown that this observer is of interest in the field of hybrid systems and systems with observability singularities. Lastly, it is shown through an example how to relax the usual matching condition by the means of this type of finite time sliding mode observer.

Observability normal forms for a class of switched systems with zeno phenomena

“…Consequently, there exists a Lyapunov function V (e) with respect to (15), (16) and (17), (18) such that:…”

“…For system of the form (3)-(4) algebraic estimator [3], [21] or step by step sliding mode observer [4], [15] work well in the continuous state estimation, because in the first equation of (3),ξ 1 is never considered. More precisely, the output derivative is considered only until n−1 in algebraic solution and the last step is a sliding mode observer of one in the step by step sliding mode observer, i.e.…”

Causal observability of nonlinear time-delay systems with unknown inputs

“…Due to the particular triangular structure of the system (11)-(12), the whole state of the system, as well as the unknown input, can be estimated in finite time using higher order sliding mode observers [7].…”

Decentralised Observation Using Higher Order Sliding Mode Techniques

“…Step-by-step vector-state reconstruction using super-twisting first order robust exact differentiators has been presented in Floquet and Barbot (2007) in which the systems are transformed to a triangular or the Brunovsky form and then the states are estimated based on the equivalent output error injection. These observers theoretically ensure finite time convergence for all system states.…”