An integral sliding mode control approach to observer-based stabilization of stochastic Itô descriptor systems.

This paper is concerned with sliding mode observer design and observer-based sliding mode controller synthesis for stochastic Itô descriptor systems. A novel integral sliding surface, which involves a product of sliding variable and a negative definite matrix, is constructed for the error system. It is shown that the product term not only has a stabilizing effect on the sliding variable, but also is beneficial to remove a restrictive assumption often employed in the sliding mode control for stochastic Itô systems. Observer-based sliding mode controllers are designed to ensure the retainability of sliding surfaces from the beginning almost surely, and the asymptotically mean square admissibility of resultant sliding motion can be determined by solving a linear matrix inequality (LMI). Two examples are performed to check the theoretical findings.