Generalized Integral Siding Mode Manifold Design: A Sum of Squares Approach

Abstract: This paper presents a general form of integral sliding mode manifold, and proposes an algorithmic approach based on Sum of Squares (SOS) programming to design generalized integral sliding mode manifold and controller for nonlinear systems with both matched and unmatched uncertainties. The approach also gives a sufficient condition for successful design of controller and manifold parameters. The result of the paper is then verified by several simulation examples and two practical applications, namely Glucose-insulin regulation problem and the unicycle dynamics steering problem are considered.