Stabilization Problem for a Class of Nonlinear MIMO Systems Based on Prescribed-Time Sliding Mode Control

In this paper, we investigate a class of nonlinear MIMO systems based on prescribed-time sliding mode control (PTSMC). In an effort to extend the concept of fixed-time theory with capability of handling more practical systems, we have developed a PTSMC based on the free-will arbitrary time (FWAT) principle of stability. We propose the FWAT sliding surfaces to improve the convergence of a nonlinear system, what is known as arbitrary convergence in control theory. According to the proposed sliding surface, the states of a system can reach the sliding surfaces (arbitrary reaching phase) within a given time interval and also can hit the origin within a predefined time (arbitrary sliding phase). Using this method, the overall stabilization time can be adjusted freely to suit the needs of the designer. Furthermore, this control method is capable of being implemented independent of any other system parameters. Lyapunov stability theory shows the stability of the proposed control scheme and the designed sliding surfaces. Finally, the efficiency of the proposed approach is demonstrated by performing on two well-known examples such that it verifies the arbitrary convergence of the designed sliding surfaces for various times in spite of revealing the designed control independency of any initial values.