Systematic approach of extracting sliding manifold in robust stabilizing of stochastic multi-input systems

Logarithmic sliding function obtained from a systematic procedure was provided for reliable variable structure control of uncertain stochastic multi-input systems so that it could guarantee global asymptotic stability of the closed loop system with probability one. Control effort, robustness of the system, and other operational characteristics may vary depending on the selected sliding manifold. In the previous research on uncertain stochastic systems, the sliding surface structure is generally known from the beginning, which could be considered as an initial restriction like a linear sliding manifold. This constraint causes the switching variable to be placed in a limited work space; therefore, resultant sliding surface is locally optimum or desirable. In another study, we had proposed a method for sliding manifold extraction through a targeted strategy with no initial restriction on its structure which, unlike other similar studies, provided a global optimality. However, the proposed method could not be used for multi-input systems and has not been further developed. In this paper, we extended this technique to be applicable for systems with multiple inputs and ensured the reachability of all the sliding surfaces. Illustrative examples are given in order to show the feasibility of the method.