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In this study, a novel method is proposed for a class of MIMO linear systems non-singular terminal sliding mode control to solve singularity problem. A state transformation matrix is designed properly to transfer a class of MIMO linear systems into a new form without changing its controllability and observability, the design method and application conditions are given. Based on it, the traditional non-singular method of second-order nonlinear systems can be used in the new form of MIMO linear systems by adjusting the dimension of coefficients appropriately. Then an example is given to validate the effectiveness of the proposed form. Stability analysis and numerical simulations show that the proposed method can guarantee system states to converge to equilibrium point with strong robustness in finite time, and the singularity problem can also be avoided appropriately.

In this paper, a class of nonlinear systems is considered, where the nominal system representation is allowed to be non-minimum phase. A sliding surface is proposed which is a function of the measured system output and an estimated state. A linear coordinate transformation is introduced so that the stability analysis of the reduced order sliding mode dynamics can be conveniently performed. A robust output feedback sliding mode control (OFSMC) is then designed to drive the system states to the sliding surface in finite time and maintain a sliding motion thereafter. A simulation example is used to demonstrate the effectiveness of the proposed method and the method is successfully applied to an inverted pendulum.