Exact differentiation and sliding mode observers for switched Lagrangian systems

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

“…The sliding motion provides an estimation of the system state, asymptotically (see e.g. [62,56,59,20,57,50,54]) or in finite time (for instance, one can 1 refer to the works of [18,19,2,32,60] for design methods based on first order sliding mode algorithms and the works of [41,4,53] for second order ones). Sliding mode observers have been shown to be a robust observation scheme in robotics [9,35,45], electrical engineering [15,60] or chemical reactors [46].…”

State observer and observability conditions for a class of hybrid continuous-discrete dynamic system

“…In [20], a Super Twisting Algorithm (STA) was used for switched system. In our case, a STA is used for the continuous part of the system.…”

“…Note that the designed method performed in [2,18], for finite time convergent observers for linear time-varying systems, can be used in our case. The estimationẐ(k − N ) can also be obtained by using left invertibility on the equation (20), one obtains:…”

“…In this case, the control strategy consists in discretizing the electrical part of the dynamics (which will be controlled by the orders of commutations) and to keep the mechanical part in continuous time. Note that, in the literature, several papers have defined observability for different classes of hybrid systems ([2, 3,4,5,7,8,20,21]). This paper concerns hybrid observer design for the following particular class of HDS:…”

Real-time estimation of the switching signal for perturbed switched linear systems

“…But concerning the estimation of the switching function, up to now very few results are concerned with such estimation problem let us mention Millnert [1980] on identification of abruptly changing systems using least-square methods (with an example of switching between two linear systems), Vu and Liberzon [2008] on left invertibility 1 and Balluchi et al [2002], Ragot et al [2003], Saadaoui et al [2006], that are providing switching function estimators. Following the previous obtained results by the authors (see ) we investigate here the structured perturbed case that is when the submodels are perturbed with an exogenous signal which is unknown but which is known to satisfy a given differential equation.…”