Observability Normal Forms

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

“…Loss of observability may locally appear in nonlinear systems because of the nonlinear structure itself [3] or due to singular inputs (i.e. inputs that make the system unobservable, see [28]).…”

“…On another hand, it can be very useful for particular application such as secure data transmission [3]. Indeed, the confidential message can be hidden in some observability singularity and one has to design a variable structure observer to recover it.…”

“…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]. Specific applications of asymptotic and finite time observers for systems with unknown inputs can be found in a large number of fields such as fault detection and identification [22,30,58,23], parameter identification [26,55], cryptography [3], or mechanical systems with Coulomb friction [13,27,47].…”

An observability form for linear systems with unknown inputs

“…Some of these applications are classical ones as fault detection and isolation (Chen et al (1996); Floquet et al (2004)), whereas other ones are more 'exotic' such as for example decoding an encrypted message (Barbot et al (2003)). The application domains have an important consequence on the assumptions claimed on the unknown inputs.…”

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].…”