A robust analysis approach for a class of uncertain BPV systems

Abstract This work deals with the robustness analysis of LPV (Linear Parameter-Varying) systems. The degree of robustness of a system makes possible to know if the defined level of performance is guaranteed or not. The robustness of a system is characterized by its capacity to reject perturbations, by criterion of speed, of precision or by taking into account a certain degree of imprecision of the model, often introduced during a necessary phase of linearization. It is then necessary to manipulate relatively sophisticated models in order to take all these parameters into account. The representation of the LPV systems is such a sophisticated modeling. Fuzzy Takagi–Sugeno, polytopic and norm-bounded representations are often used to describe the behavior of nonlinear dynamics of the system. This paper proposes a generic model that encompasses these representations (fuzzy TS, polytopic and norm-bounded). This generic model is denoted uncertain BPV (Bi-linear Parameter Varying). A robustness analysis technique, allowing the generation of a robustness criterion, is then proposed. It can be applied to the case of state or output feedback, as well as to paremeter-dependent controllers. The concept of D -stability is considered and the tools are expressed in terms of LMI .