A Novel Sliding Mode Control for a Class of Affine Dynamic Systems

This paper proposes a novel sliding mode control (SMC) method for a class of affine dynamic systems. In this type of systems, the high-frequency gain matrix (HFGM), which is the matrix multiplying the control vector in the dynamic equation of the sliding variables vector, is neither deterministic nor positive definite. This case has rarely been covered by general SMC methods, which perform well under the condition that the HFGM is certain or uncertain but positive definite. In this study, the control law is determined by solving a nonlinear vector equation instead of the conventional algebraic expression, which is not applicable when the HFGM is uncertain and non-positive definite. Theorems with some relaxed system parametric uncertainty assumptions are proposed to guarantee the existence and uniqueness of the solution, and proofs of them, based on the principle of the convex cone set, are given in the text. The proposed control strategy can be easily applied in practice, and the chattering caused by the discontinuous control can be suppressed, as it can in general SMCs. The proposed controller was used in two affine dynamic systems, and the simulation results demonstrate its effectiveness.