A generalized regular form for multivariable sliding mode control (Q5933552)

A smooth multi-input multi-output control system is considered. The problem of finding a diffeomorphic state space transformation in order to put the original system into an appropriate regular form is studied. The proposed procedure is: first, to transform the original system into a system with full rank gain matrix; next, using a differential geometric approach to define conditions for existence of a regular form. This regular form is an extension of the one proposed by \textit{A. G. Lukyanov} and \textit{V. I. Utkin} [Autom. Remote Control 42, No. 4, 413-420 (1981; Zbl 0466.93016)]. On the basis of this regular form, the stabilization problem via a sliding mode strategy is studied. In order to overcome the so-called chattering phenomenon, a nonlinear gain for the corresponding signum function is introduced.