Some new application of VSS theory to the control of uncertain nonlinear systems

The approximability property of a variable-structure system (VSS) can be thought as a validation of the axiomatic Filippov theory by means of the usual ordinary differential equation methods when, due to some nonideal behaviors, the system trajectory lies in a bounded neighborhood of the sliding manifold. An extension of the concept of approximability, called generalized approximability, is introduced. The main feature of this new concept lies in the fact that in some cases the existence and unicity of the equivalent control can be dispensed with, to guarantee the approximability property for the Filippov solution of a discontinuous control system. An asymptotic linearization problem, namely, asymptotic linearization through nonlinear transformation and dynamical feedback, is introduced