Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi–Sugeno's form

This article addresses the stabilisation of non-linear systems represented by a discrete-time Takagi–Sugeno model. Based on an extended non-quadratic Lyapunov function and a non-parallel distributed compensation (non-PDC) law, some additional slack matrices are introduced. Compared with the existing methods, which collect the interactions among the subsystems into a sequence of collection matrices, the new method re-collects the newly introduced slack matrices into another collection matrix. In this way, a stability result more relaxed than some existing ones are obtained. Further, the convexity of the fuzzy blending rules is utilised, with a further improved result obtained. The corresponding robust stability results are also proposed. The effectiveness of the new results is validated by two simulation examples.