A New Fuzzy Lyapunov Approach to Non-Quadratic Stabilization of Takagi-Sugeno Fuzzy Models

Abstract

In this paper, new non-quadratic stability conditions are derived based on the parallel distributed compensation scheme to stabilize Takagi-Sugeno (T-S) fuzzy systems. We use a non-quadratic Lyapunov function as a fuzzy mixture of multiple quadratic Lyapunov functions. The quadratic Lyapunov functions share the same membership functions with the T-S fuzzy model. The stability conditions we propose are less conservative and stabilize also fuzzy systems which do not admit a quadratic stabilization. The proposed approach is based on two assumptions. The first one relates to a proportional relation between multiple Lyapunov functions and the second one considers an upper bound to the time derivative of the premise membership functions. To illustrate the advantages of our proposal, four examples are given.

Enhanced LMI conditions for quadratic fuzzy control design

“…Since the separate stabilization of the local modes does not ensure the stability of the overall system, a range of stability conditions was developed (see e.g. [1], [3], [8], [15]), most of them relying on the feasibility of an associated system of linear matrix inequalities (LMI). Therefore, the state control based on fuzzy TS system model gives control structures which can be designed using methods derived from equivalent LMIs (some principles and results are reported e.g.…”

Stabilizing fuzzy static output control for a class of nonlinear systems

“…Unfortunately, it is also known that the separate stabilization with respect to local TS models does not ensure the stability of the overall system, and global design conditions have to be used to guarantee the global stability and control performance, using the control policy based on the parallel distributed compensator, where the control law shares the same fuzzy rules the TS system. In that way, a range of stability conditions have been developed for TS fuzzy systems [1], [5], [8], [11], [17], [19], relying mostly on the feasibility of an associated set of linear matrix inequalities (LMI) [2]. An important fact is that the stability problem is a standard feasibility problem with several LMIs, potentially reformulated such that the feedback gains can be solved numerically.…”

Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent

“…Many works in the literature are devoted to decreasing the conservativeness of these LMIs in order to apply them to a wider class of systems Abdelmalek et al, 2007;Bernal and Hušek, 2005). Another possible solution is to use nonlinear local subsystems for the T-S model.…”