Global stabilization by output feedback: examples and counterexamples

Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems

“…As shown in [17] in the context of global asymptotic stabilization of the origin, the tracking problem under consideration might be unsolvable. Consequently, we need to impose some restrictions on the functions f i .…”

“…Following the domination approach, we focus on the dominant part of system (17) in the scaled coordinate (18), i.e. a chain of integrators, with state X = (X 1 , .…”

“…a systemη = f (η, u) with output y = h(η), 2. a bounded state and input reference trajectory (η r , u r ), available at each time but not ahead of time design an output feedbackẇ = θ(w, y, η r ), u = ϕ(w, y, η r ) which ensures global convergence or, asymptotic closeness (in a sense to be specified) of η to η r . This problem is challenging since, as shown in [17], controllability and observability are not sufficient to guarantee the existence of a solution, as is the case for linear systems. Hence, some restrictions have to be imposed on the nonlinear function f .…”

Enlarging the basin of attraction by a uniting output feedback controller

“…All these previous works focus on uniting local and global controllers. However, it is well-known that there are systems which cannot be globally stabilized, for instance unstable linear systems with bounded control [16] and the examples in [10]. For those systems, instead of requiring controllers with global stability properties, we can aim at designing controllers for semi-global asymptotic stabilization.…”

Cascade-Based Controlled Attitude Synchronization and Tracking of Spacecraft in Leader-Follower Formation

“…The ability to control two coupled systems separately is called separation principle and is known not to hold in general for nonlinear systems (see e.g. [24]). This is where cascades theory enters in play.…”