“…However, it is important to note that although the use of a polynomial Lyapunov matrix yields the sufficient and necessary conditions for stability analysis 1 Marco A. C. Leandro is with The Electronics Engineering Division, Instituto Tecnológico de Aeronáutica, DCTA-ITA-IEE, São José dos Campos, SP, 12228-900, Brazil (email:marcoacleandro@gmail.com) 2 José R. Colombo Júnior is with The Electronics Engineering Division, Instituto Tecnológico de Aeronáutica, DCTA-ITA-IEE, São José dos Campos, SP, 12228-900, Brazil (email:colombojrj@gmail.com) 3 Karl Heinz Kienitz is with The Electronics Engineering Division, Instituto Tecnológico de Aeronáutica, DCTA-ITA-IEE, São José dos Campos, SP, 12228-900, Brazil (email:kienitz@ita.br) [9], [10], so far, there are no extensions to the use of these conditions for the synthesis of a robust gain. Given this, the synthesis of a robust gain for polytopic uncertain systems can be approached with QS [11] or using a Lyapunov matrix depending on the affine form on the parameter and LMIs relaxations [12], [13], [14], [6], [5], [15] in many cases involving the search for a scalar parameter [16].…”