Robust quadratic stabilizability of non-homogeneous Sugeno's systems ensuring completeness of the closed-loop system

This paper addresses the problems of quadratic stability and stabilizability of a class of uncertain nonlinear systems. The model of the system is a non-homogeneous Tagaki-Sugeno-Kang type. One of the originality of the model is that the premise part of the rules include control vector. Conclusions and premise parameters uncertainties are handled. We provide necessary and sufficient conditions for the quadratic stability problem using linear matrix inequalities (LMI). It is proved that local quadratic stability does not necessary ensure global stability. Sufficient condition involving LMI is also derived to solve the analysis problem of completeness of a given closed-loop system. Then, we formulate the synthesis problem which guarantee stability and completeness (i.e. logical consistency of the closed loop system). Computational issues of the synthesis problem are discussed.