Functional observer-based finite-time adaptive ISMC for continuous systems with unknown nonlinear function

This paper is concerned with functional observer-based finite-time adaptive integral sliding mode control (ISMC) for continuous systems with unknown nonlinear function. First, a novel finite-time ISMC framework is established based on the functional observer whose parameters can be directly found. Second, an adaptive compensator is designed to counteract the effect of the unknown nonlinear function such that the composite integral sliding mode controller ensures that the closed-loop system reaches boundedness in a predefined finite time. Moreover, some sufficient conditions in the form of matrix inequalities are proposed to guarantee the finite-time boundedness with H_∞ performance (FTB-H_∞) over the sliding phase and the reaching phase of the closed-loop system. Then the FTB-H_∞ conditions over the whole finite-time interval are also provided. Due to introducing more degrees of freedom in the functional observer, the designed finite-time integral sliding mode controller is more flexible and less conservative. Finally, a simulation example is given to show the validity of the proposed method.