This paper considers a class of uncertain nonlinear systems exactly described by Takagi-Sugeno (T-S) fuzzy models, with or without matched uncertainties and/or disturbances, within an operating region in the state space. Considering the plant subject to actuator saturation is proposed, a switched control design method such that the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate, for all initial conditions in a region obtained in the design procedure, that is within a given operating region. Moreover, an exact representation of the minimum function using signal functions is presented. Therefore, it is offered a bridge between the switched control and variable structure control laws, because they are usually based on minimum and signal functions, respectively. Considering the well-known approximation of the signal function by a sigmoid function, this paper introduces the 'smooth minimum' function. The smooth minimum function allowed the design of 'smooth switched' control laws, without chattering, for the aforementioned class of systems. The proposed smooth switched control laws guarantee the uniform ultimate boundedness of the controlled systems. Design examples and simulation results illustrate the control design procedures and the effectiveness of the proposed control laws. Future researches in this subject may explore the presented relationship between the switched control and variable structure control laws, in order to obtain new useful control laws. of the system by choosing a feedback gain, belonging to a given set of gains, which minimizes the time derivative of a Lyapunov function. The design conditions are represented by LMIs, which can be solved in a computationally efficient manner [15,16].Frequent and/or abrupt changes of the feedback gains, however, can generate control signal chattering. Control signal chattering is a generally undesirable phenomenon in real systems. Different control strategies try to avoid the chattering problem, for instance, in sliding mode control [17][18][19][20][21][22][23][24], to name a few, in adaptive control [25][26][27], and in control of switched linear systems [28][29][30].In this context, this paper extends the methodology proposed in [13,14] for uncertain T-S fuzzy models, based on [31,32], taking into account actuators saturation. Additionally, an invariant region E.P; 1/ is estimated, in which for every x.0/ 2 E.P; 1/, the state vector of the controlled system x.t/, t > 0 is in a given operation region where the T-S fuzzy model exactly describes the nonlinear system and also the equilibrium point of the controlled systems is locally asymptotically stable with an adequate decay rate. Moreover, 'smooth switched' control laws are proposed, without using the plant membership functions. A key point of the new control laws is a proposed exact representation of the minimum function using signal functions. Considering that the minimum functions are largely used in switched control laws [13,14,[28][29][30] and the s...

This manuscript proposes a local H ∞ switched controller design for a class of uncertain nonlinear plants described by Takagi-Sugeno (T-S) fuzzy models with unknown membership functions. The control design requires only the lower and upper bounds of the system nonlinearities and of the system linear parameters, which can depend on uncertain parameters. The switched control law chooses a state-feedback controller gain, which belongs to a given set of gains, that minimizes the time derivative of a quadratic Lyapunov function. This procedure eliminates the necessity of finding the membership function expressions to implement the control law, guarantees an H ∞ performance and ensures that the state trajectory remains within a region in which the T-S fuzzy model is valid. Due to the H ∞ control design, that frequently results in very large control inputs, it is considered that the switched control law is subject to actuator saturation. Finally, two examples are presented. The first example studies the control of a chaotic Lorenz system. It shows that, for disturbances with large magnitude, the proposed procedures provided better results than the obtained with another recent method found in the literature, that considers full access to the membership functions. In the second example, a practical implementation of an active nonlinear suspension control system, considering an uncertain bounded mass and a fault in the actuator, confirms the effectiveness of the proposed approach.

In recent years, the study of systems subject to time-varying parameters has awakened the interest of many researchers. The gain scheduling control strategy guarantees a good performance for systems of this type and also is considered as the simplest to deal with problems of this nature. Moreover, the class of systems in which the state derivative signals are easier to obtain than the state signals, such as in the control for reducing vibrations in a mechanical system, has gained an important hole in control theory. Considering those ideas, we propose sufficient conditions via LMI for designing a gain scheduling controller using state derivative feedback. The D-stability methodology was used for improving the performance of the transitory response. Practical implementation in an active suspension system and comparison with other methods validates the efficiency of the proposed strategy.

This paper investigates the robust control problem of continuous-time uncertain switched linear systems, using only a switching strategy depending on the plant output. The proposed method is based on linear matrix inequalities (LMIs). A set of slack variables is introduced to reduce the design conservatism, and new sufficient LMI conditions for the synthesis of the controllers are presented. Two examples show that the proposed method has an adequate performance even in situations when the matrices of the linear subsystems

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Um projeto de controle H1 chaveado para uma classe de sistemas n˜ao lineares incertos descritos por modelos fuzzy Takagi-Sugeno ´e apresentado neste trabalho. A metodologia apresentada baseia-se na constru¸c˜ao de um vetor de estado expandido, formado pelo vetor de estado e pelo sinal de controle. Al´em disso, a lei de controle chaveada elimina a necessidade de usar as fun¸c˜oes de pertinˆencia na sua implementa¸c˜ao e as condi¸c˜oes de projeto garantem apermanˆencia das trajet´orias dos estados e do sinal de controle dentro de uma regi˜ao de opera¸c˜ao do sistema. Por fim, o esquema de controle elimina a possibilidade de uma descontinuidade no sinal de controle.

In the robust control literature it is usual to propose the design of the controller for the system using the polytope vertices with the maximum and minimum values of each uncertainty. Although this proposal is reasonable, it can be conservative since it can include an area of the convex region that the system does not operate. This article proposes to choose vertices of polytope that reduces the area of the convex region of the plant to make the controller design procedure less conservative. A robust switched controller will be designed for the sensorfault 2D ball balancer system, using vertices of the polytope with a convex area smaller than that traditionally proposed, to demonstrate that it is less conservative. It will be presented a method to choose the vertices for the particular case in which an uncertainty depends on a variable γ and the other depends on its inverse γ −1. The designed controller was implemented to prove its operation in practice. Resumo: Na literatura, para abordar o problema do controle robustoé usual propor o projeto de controle para o sistema utilizando os vértices do politopo considerando os valores máximos e mínimos de cada incerteza. Embora essa proposta seja razoável, ela pode ser conservadora já que pode incluir umaárea da região convexa em que o sistema não opera. Esse artigo propõe uma metodologia para a escolha de vértices do politopo que reduz aárea da região convexa da planta do sistema para tornar o projeto de controle menos conservador. Um controlador robusto chaveado foi projetado para o sistema 2D ball balancer considerando a possibilidade de falha no sensor, utilizando vértices do politopo comárea convexa menor do que a que seria proposta tradicionalmente, para demonstrar queé menos conservador. Será apresentado um método para a escolha dos vértices para o caso particular em que uma incerteza depende de uma variável γ e a outra depende de sua inversa γ −1. O controlador projetado foi implementado para comprovar seu funcionamento na prática.