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A generalized regular form for multivariable sliding mode control. (English) Zbl 0978.93015
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 A. G. Lukyanov and 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.

93B12 Variable structure systems
93D15 Stabilization of systems by feedback
93C35 Multivariable systems, multidimensional control systems
93B17 Transformations
93B29 Differential-geometric methods in systems theory (MSC2000)
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