Integral Sliding-Mode Control of Piecewise Linear systems

This paper proposes a dynamic integral sliding-mode control approach for a class of nonlinear systems based on piecewise affine linear models. A general nonlinear system is first modeled equivalently as a uncertain piecewise affine linear system with norm-bounded approximation errors. Based on the equivalent piecewise affine linear system, a dynamic integral sliding-mode control (DISMC) scheme is then proposed. The scheme holds a favorable characteristic in the sense that it allows different input matrices in each subregion, which makes the proposed approach more relaxed than many existing methods. Moreover, a constructive procedure of the DISMC via convex optimization is presented. Finally, a numerical example is provided to demonstrate the advantages and effectiveness of the developed approach.