Global Finite Time Stabilization of a Class of Uncertain MIMO Nonlinear Systems

Abstract

It is aimed to obtain global finite time stabilization of a class of uncertain multi-input–multi-output (MIMO) nonlinear systems in the presence of bounded disturbances by applying nonsingular terminal sliding mode controllers. The considered nonlinear systems consist of double integrator subsystems which interact with each other. In the proposed methods, new terminal sliding surfaces are introduced along with design of proper control inputs. The terminal sliding surfaces are defined such that the global finite time stability of sliding mode dynamic is attained. The control inputs are designed to steer the states into sliding motion within finite time and retain them on the terminal sliding surfaces. The presented approaches guarantee the finite time convergence of states with low sensitivity to their initial values. The convergence rate could be adjusted by proper choice of existing arbitrary parameters in the suggested control schemes. Three numerical simulation examples including van de Pol system and two robotic manipulators are provided to confirm the applicability and effectiveness of the proposed control schemes.