Sliding mode observers. Tutorial

Global finite-time observers for non linear systems

“…There exists several methods achieving finite-time convergence, e.g. sliding mode observers (see [15,16]), moving horizon observer (see [17]), but some of these are not continuous like sliding mode observers. We consider here continuous finite-time observer.…”

On sliding mode observers for systems with unknown inputs

“…Most of the sliding mode observer designs for (10) are based on a step-bystep procedure using successive filtered values of the so-called equivalent output injections obtained from recursive first order sliding mode observers (see e.g. [1,8,9,19,26,36]). However, the approximation of the equivalent injections by low pass filters at each step will typically introduce some delays that lead to inaccurate estimates or to instability for high order systems.…”

“…The concept of sliding mode control [12,27,33] has been extended to the problem of state estimation by an observer, for linear systems [33], uncertain linear systems [11,35] and nonlinear systems [1,9,29]. Using the same design principles as for variable structure control, the observer trajectories are constrained to evolve after a finite time on a suitable sliding manifold by the use of a discontinuous output injection signal (the sliding manifold is usually given by the difference between the observer and the system output).…”

A Canonical Form for the Design of Unknown Input Sliding Mode Observers

“…One can refer to the works [15,19,33] for linear systems or to [1,7,8,35] for nonlinear systems. Applications can be found in fault detection and isolation [16] or in cryptography [2].…”

“…The concept of sliding mode control [11,27,32] has been extended to the problem of the state estimation by an observer, both for linear [10,32] and nonlinear systems [1,8,28,34]. Using the same design theory as variable structure control laws, the observer trajectories are constrained to evolve after a finite time on a suitable sliding manifold, by the use of a discontinuous output injection (the sliding manifold is usually given by the difference between the observer and the system output).…”