Relaxed stability and stabilisation conditions for continuous-time Takagi–Sugeno fuzzy systems using multiple-parameterised approach

摘要

This study deals with the problem of stability analysis and control design for continuous-time Takagi-Sugeno fuzzy systems. Based on generalised fuzzy Lyapunov function (FLF) and fuzzy controller, relaxed stability and stabilisation conditions in terms of linear matrix inequalities are obtained. The generalised FLF is homogeneous polynomially parameter dependent on MFs with arbitrary degree. As the degree of the Lyapunov function increases, the conservatism of the obtained stability and stabilisation conditions is gradually reduced. In addition, it can be proved that the conditions generated in this study can include the existing ones found in the literature as special cases. Compared with the existing methods, no additional slack variables are introduced in stability analysis, and hence the same or less conservative results can be obtained with a lower computational cost. Numerical examples illustrate the effectiveness of the proposed method.