Stability analysis of T–S fuzzy control systems using parameter-dependent Lyapunov function
The system stability of T–S fuzzy-model-based control systems with a parameter-dependent Lyapunov function (PDLF) is investigated. As PDLF approach includes information of the membership function (time derivatives of membership functions), it has been reported that relaxed stability conditions can be achieved compared to the parameter-independent Lyapunov function (PILF). To investigate the system stability, the non-linear plant is represented by a T–S fuzzy model. Various non-parallel distribution compensation (PDC) fuzzy controllers, which can better utilise the characteristic of the PDLF, are proposed to close the feedback loop. To relax the stability conditions, an improved PDLF is employed. Some inequalities are proposed to relate the membership functions and its time derivatives, which allow the introduction of some slack matrices to facilitate the stability analysis. Stability conditions in terms of linear matrix inequalities are derived to aid the design of stable fuzzy-model-based control systems. Simulation examples are given to illustrate the effectiveness of the proposed non-PDC fuzzy control schemes.
