Stabilization Conditions Of Fuzzy Systems Under Persistent Perturbations And Their Application In Nonlinear Systems

摘要

The rejection of perturbations is a classical problem in control theory. Part of the interest in the rejection of persistent disturbances is focused on those perturbations affecting nonlinear systems [Chen, C.W., 2006. Stability conditions of fuzzy systems and its application to structural and mechanical systems. Advances in Engineering Software 37(9), 624-629; Isidori, A., Astolfi, A., 1992. Disturbance attenuation and H_∞-control via measurement feedback in nonlinear systems. IEEE Transactions on Automatic Control 37(9), 1283-1293]. This paper, firstly, analyzes some literature contributions which tackle the problems of using fuzzy models as representations of the nonlinear behaviour of the real system-and shows the drawbacks of these methods. Secondly, a method for designing parallel distributed compensation fuzzy state-feedback controllers is proposed. This new approach is based on minimizing the 1-norm between the disturbance input signal and output signal. Specifically, an upper bound on this norm, the ★-norm, is minimized, which, unlike the 1-norm, can be formulated in terms of linear and bilinear matrix inequalities. This novel contribution presents two main advantages with respect to previous works-firstly, it considers a priori bounds on the applied persistent perturbation. Secondly, it provides a minimized upper bound on the output. The proposed method has been tested on a mechanical system with nonlinear behaviour. By means of this example, we show that the minimization of the ★-norm can also limit the control actions, if they are very large.