Nonquadratic local stabilization of T-S fuzzy systems via improved slack-variable-free relaxation technique under limited operating region

Abstract

This paper aims to investigate the problem of nonquadratic local stabilization and disturbance attenuation for Takagi-Sugeno (T-S) fuzzy systems under the limited operating region of premise variables. To derive less conservative local stabilization conditions, this paper first proposes a parameterized linear matrix inequality (PLMI) formulation method that enables both the nonquadratic Lyapunov function and the non-parallel distributed compensation (non-PDC) control scheme. Specifically, in the PLMI formulation, the time derivatives of fuzzy basis functions are addressed without any boundary assumptions and by avoiding excessive use of inequality constraints and slack variables. Moreover, an effective relaxation technique is proposed to obtain a finite set of LMIs from PLMIs in a less conservative way without extra slack variables. Finally, three examples are provided to illustrate the effectiveness of the proposed method.