This study introduces the fuzzy Lyapunov function to the fuzzy PID control systems, modified fuzzy systems, with an optimized robust tracking performance. We propose a compound search strategy called conditional linear matrix inequality (CLMI) approach which was composed of the proposed improved random optimal algorithm (IROA) concatenated with the simplex method to solve the linear matrix inequality (LMI) problem. If solutions of a specific system exist, the scheme finds more than one

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... at a time, and these fixed potential solutions and variable PID gains are ready for tracking performance optimization. The effectiveness of the proposed control scheme is demonstrated by the numerical example of a cart-pole system. key words: modified fuzzy systems, fuzzy Lyapunov function, self-tuning PID, conditional linear matrix inequality, improved random optimal algorithm