Dissipative sliding mode tracking control for discrete-time singular T-S fuzzy systems via a preview target mechanism

This study focuses on the dissipative sliding mode preview tracking control (SMPTC) of discrete-time singular T-S fuzzy systems (STSFSs) via a preview target mechanism. Due to the presence of singular matrix and input matrices with fuzzy rules in the system, the existing preview control approaches cannot be directly adopted. As a result, a novel singular augmented error system (AES) is derived based on a general method. Furthermore, the tracking problem has been translated into the stabilisation of singular AES. A linear sliding mode surface (SMS) is proposed for singular AES, and a suitably SMPTC law is presented. Sufficiency conditions for relaxation are derived to guarantee that the sliding mode dynamics is admissible with the dissipative criterion, and the sliding mode region (SMR) can be reached. The difference singular matrix is fully considered in the whole design process such that the derived conditions can be checked easily. Finally, two examples have shown the effective tracking of the original output signal of system by utilising the proposed SMPTC law.