A variational characterization of the sliding mode control processes

This paper deals with a new theoretic description of some classes of the conventional sliding mode control processes. We use a variational characterization of the first-order variable structures dynamics and extend the corresponding state space formalism. A trajectory of the original systems can finally be specified as a result of a particular system optimization procedure applied to the original model. The presented variational theory of some sliding mode-type control systems is motivated by an alternative approach to the control design procedure. The mathematical tool of the sliding mode systems theory presented in our paper constitutes a formal extension of the classic Fillipov results.