A design of sliding mode control for uncertain T-S fuzzy systems with multiple input matrices

This paper investigates how to design a sliding mode surface and construct a sliding controller to stabilize a uncertain T-S fuzzy system with multiple input matrices and matched disturbances. The method proposed in this paper can expand the effective scope of sliding mode control into uncertain fuzzy systems even if there are not assumptions of input matrices. In order to expand the effective scope of controlled systems, firstly, transform the form of input matrices of system plants into a new input matrix B. Secondly, design a new sliding mode surface according to all the input matrices. It contains q sub-sliding surfaces. The number q is the column number of input matrix B. Thirdly, according to sliding mode theorem, the equivalent controller can be deduced. But, it may be nonexistence. A judgment criterion for the existence of the controller is given as a lemma. By use of the proposed sliding surface, a new sliding controller is constructed. It can settle the confliction difficult between sliding surface and input matrices. And it can make the system reach the sliding surface and keep on it thereafter. At last, two examples are given to illustrate the effectiveness of this paper.