Robust control strategies for a class of nonlinear systems with an ill-defined relative degree

Parameter Homotopy Continuation for Feedback Linearization of Non-Regular Control-Affine Nonlinear Systems

“…The problem of ill-defined relative degree is well-known in literature. For example, most underactuated systems are not fully feedback linearizable, and smooth feedback stabilization to a single equilibrium point is not possible [10,14,15,1]. Another case of the nonlinear system with ill-defined relative degree consideredm is DC-motor in bidirectional operation when the armature current approaches to zero [24].…”

“…In one of recent publications [14] the applicability of a composite control scheme consisting of heuristic-based approximate linearization and backstepping design for a nonlinear system is investigated. Another type of solution is presented in [1] where inverse Lyapunov approach in conjunction with the energy shaping technique is applied to ball and beam system.…”

“…Applying condition (14) to (24), we obtain that rank D ξ,λ Ψ = m. Hence, according to the implicit function theorem, arguments similar to the case r i = 1 can be made for the curve γ(t) = (ξ(t),λ(t)), which is defined implicitly by the equation Ψ(ξ,λ, t) = 0.…”