This paper is concerned with the design of state-feedback switched controllers for a class of uncertain nonlinear plants described by Takagi-Sugeno (T-S) fuzzy models. The proposed methodology eliminates the need to find the membership function expressions to implement the control law, which is relevant in cases where the membership function depends on uncertain parameters. The design of the switched controllers is based on a minimum-type Lyapunov function and the minimization of the time derivative of this Lyapunov function. The conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities (BMIs) that has been solved by the path-following method. A numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure. Index Terms-Bilinear matrix inequalities (BMIs), control of uncertain nonlinear systems, linear matrix inequalities (LMIs), switched control, Takagi-Sugeno (T-S) fuzzy model.

This paper proposes a new switched control design method for some classes of linear time-invariant systems with polytopic uncertainties. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology offers less conservative alternative than the well-known controller for uncertain systems with only one state feedback gain. The control design of a magnetic levitator illustrates the procedure.

The paper proposes a new design method based on linear matrix inequalities (LMIs) for tracking constant signals (regulation) considering nonlinear plants described by the Takagi-Sugeno fuzzy models. The procedure consists in designing a single controller that stabilizes the system at operation points belonging to a certain range or region, without the need of remaking the design of the controller gains at each new chosen equilibrium point. The control system design of a magnetic levitator illustrates the proposed methodology.

The paper proposes a new switched control design method for some classes of uncertain nonlinear plants described by Takagi-Sugeno fuzzy models. This method uses a quadratic Lyapunov function to design the feedback controller gains based on linear matrix inequalities (LMIs). The controller gain is chosen by a switching law that returns the smallest value of the time derivative of the Lyapunov function. The proposed methodology eliminates the need to find the membership function expressions to implement the control laws. The control designs of a ball-and-beam system and of a magnetic levitator illustrate the procedure.

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...