Stability Analysis of Fuzzy Control Systems via the Method by Haddad

Abstract

Fuzzy control systems can be regarded as nonlinear systems due to the input-output relations of the controller. Hence, various stability analysis methods for nonlinear systems have been successfully applied to fuzzy control systems. But such studies investigate certain specific fuzzy control systems only to get ad hoc results. A possible strategy to cope with such a situation is to increase the number of usable tools so as to cover a wide range of systems. This prompts us to add an alternative to the possible analysis tools. In this paper, we explore a stability test method by Haddad for fuzzy control systems. This method has the merit in that it can be used for many types of nonlinear systems, because it does not need any constraints to the nonlinear property such as sector conditions. The method boils down to a nonlinear optimization problem, which is hard to solve. Using the local monotonicity property of input-output relation of the controller employed here, however, we resolve this problem to obtain an effective stability test. Numerical examples are provided to show comparison with the circle condition and simulation results.