Local state-feedback stabilization of continuous-time Takagi-Sugeno fuzzy systems

Author(s)

Gomes, Izabella O. ; Oliveira, Ricardo C. L. F. ; Peres, Pedro L. D. ; Tognetti, Eduardo S.

• Document type: Journal article
• Source: IFAC PAPERSONLINE; v. 53, n. 2, p. 6-pg., 2020-01-01.

Abstract

This paper deals with the problem of local state-feedback stabilization for continuous-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. The approach is based on a polytopic representation for the gradient of the membership functions but, differently from most of the available methods, bounds for the time-derivatives of the membership functions are not required. A two step strategy is proposed for the control design. First, a sufficient condition provides a stabilizing state-feedback gain for the dual system. Although there is no guarantee of stability for the original system, the controller is used as an initial condition for the second step of the method. If a feasible solution is found, a stabilizing state-feedback controller and an estimate of the domain of attraction are certified by means of a fuzzy Lyapunov function with polynomial dependence on the membership functions. The proposed conditions, given in terms of parameter-dependent linear matrix inequalities (LMIs) with a scalar search, can be solved by LMI relaxations with optimization variables considered as homogeneous polynomials of fixed degree. Examples based on T-S models borrowed from the literature illustrate that the method performs better than other existing approaches in terms of providing stabilizing gains associated with larger estimates for the domain of attraction. Copyright (C) 2020 The Authors. (AU)

• FAPESP's process: 17/18785-5 - Parameter-Dependent Linear Matrix Inequalities Applied to Stability Analysis and Synthesis of Controllers and Filters for Uncertain Dynamic Systems
• Grantee: Pedro Luis Dias Peres
• Support Opportunities: Regular Research Grants