In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers.
A new stability analysis and design of a fuzzy switching control based on uncertain Takagi-Sugeno fuzzy systems are proposed. The fuzzy system adopted is composed by a family of local linear uncertain systems with aggregation. The control design proposed uses local state feedback gains obtained from an optimization problem with guaranteed cost performance formulated in the context of linear matrix inequalities and a fuzzy switching scheme built from local Lyapunov functions. The global stability is guaranteed by considering a class of piecewise quadratic Lyapunov functions. Examples are given to illustrate the applicability of the proposed approach. Neste trabalho, uma nova análise de estabilidade e projeto de controle fuzzy chaveado baseado em sistemas fuzzy Takagi-Sugeno com incertezas são propostos. O sistema fuzzy adotado é composto por uma família de sistemas lineares incertos locais com agregação fuzzy. O projeto de controle proposto utiliza ganhos de realimentação de estado locais obtidos da solução de um problema de otimização com desempenho de custo garantido formulado em termos de desigualdades matriciais lineares e um esquema de chaveamento fuzzy baseado em funções de Lyapunov, que são usadas quando a trajetória do estado do sistema está na fronteira de subespaços definidos do espaço de estado. A estabilidade global é garantida considerando uma classe de funções de Lyapunov quadráticas por partes. Exemplos ilustram a aplicação da abordagem proposta
(1964) for an analytical treatment about the Hermite-Biehler Theorem and a generalization of this theorem to arbitrary entire functions in an alternative way of the Pontryagin's method. 2 See Ahlfors (1953) and Titchmarsh (1939) for a detailed exposition.
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