Higher order sliding mode based finite-time order zeroing control for MIMO LTI systems

This paper introduces a control method for finite time stabilization of continuous-time controllable linear time invariant multiple-input multiple-output systems. The proposed approach uses higher order sliding mode control to reduce the system order to zero and thus providing the system states to reach the origin in finite time. Such control is called finite time order zeroing control, because it annihilates all sliding variables and their associated derivatives in finite time, while system states converge to equilibrium point. Sliding manifold reaching control uses quasi-continuous control functions. Properties of the proposed control system are demonstrated on a simulation example of a real system model.