Switching surface design via linear matrix inequality and Ackermann’s formula for a linearized inverted pendulum system

One of the most important steps to design sliding mode control (SMC) is to design switching surface. Many methods have been developed to design the SMC. Two different approaches for the design of switching surface for a linearized inverted pendulum system have been presented in this paper. In the first method (Switching surface design via Linear Matrix Inequality (LMI)) a unique design method is proposed, which characterizes linear switching surface via LMI gave the designer some usefulness in the computational aspect, so that the switching surface for even higher-order systems can be easily calculated through this method. In the second method (Switching surface design via Ackermann’s formula) which proposes a scalar sliding mode control design depends on the desired eigenvalues and the controllability matrix to achieve the desired sliding mode control performance with respect to its flexibility of solution.