Improvement of Slack Variable-Free Relaxation Method and its Application to Control Design of T-S Fuzzy Systems

The relaxation method of Tuan et al. (2001, Theorem 2.2) has been used in various studies to deal with parameterized linear matrix inequalities (PLMIs) without excessively increasing computational complexity. Inspired by this point, this paper proposes an improved relaxation method that can further reduce the conservatism of Tuan et al. (2001, Theorem 2.2) despite no additional slack variables, as well as reduce the number of LMIs (and LMI rows). To be specific, the reduction of both conservatism and computational complexity is verified through the well-known stabilization problems of both continuous-time and discrete-time T-S fuzzy systems, which shows the potential of the proposed method for its extension to other PLMI-based stabilization conditions.