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This paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. A novel augmented multi-indexed matrix approach is proposed to implement new right-hand-side slack variables technique for the homogenous polynomial setting. Combining with the Finsler lemma with homogenous-matrix Lagrange multipliers, convergent linear-matrix-inequality (LMI) relaxations for stability analysis are proposed by using the generalization of the Polya theorem for the case of positive polynomials with matrix-valued coefficients. A new type of state-feedback controller, namely, the homogeneous polynomially nonquadratic control law (HPNQCL), is developed to conceive less-conservative stabilization conditions. The obtained stability and stabilization conditions are further relaxed by using the proposed right-hand-side slack variables technique. Moreover, the advantages over the existing control schemes are certificated in theory. Three numerical examples are also provided to illustrate the effectiveness of the proposed methods.
Zhang et al. (2011) studied this question.