Chattering Free Robust Control for Nonlinear Systems

A new design method fully using the sliding manifold information is proposed to achieve a chattering free nonlinear robust control law. Guaranteed asymptotic stability is proven using the Lyapunov second theorem and the invariance principle. An explicit time varying feedback gain derived according to the global stability and sliding manifold variations is proven to be uniquely solvable based on the Perron-Frobenius theorem. The proposed nonlinear controller, which relies on the nominal system only, has the following advantages: 1) it maintains the benefits of the variable structure control which drives the system along a specified sliding surface with guaranteed stability under the bounded functional and parametric uncertainties, as well as drives the system reaching the sliding manifold in a finite time; 2) the proposed controller which eliminates the discontinuity does not induce chattering as in the variable structure control; and 3) theoretical and numerical studies in this paper show that the proposed control methodology is superior to traditional variable structure controls in terms of smooth transient performance and saturation protection for the large initial gain.