This paper is concerned with non-quadratic stabilization of continuous-time Takagi-Sugeno (TS) models. The well-known problem of handling time-derivatives of membership functions (MFs) as to obtain conditions in the form of linear matrix inequalities (LMIs) is overcome by reducing global goals to the estimation of a region of attraction. Instead of parallel distributed compensation (PDC), a non-PDC control law is proposed according to the non-quadratic nature of the Lyapunov function. Examples are provided to show the advantages over the quadratic and some non-quadratic approaches.

This paper deals with Takagi-Sugeno (T-S) systems stabilization based on dynamic output feedback compensators (DOFC). In fact, only few results consider DOFC for T-S systems and most of them propose quadratic Lyapunov stability function to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and enhance the closed-loop transient response, we provide for T-S uncertain closed-loop systems non quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of linear matrix inequalities (LMI). Afterward, the DOFC is designed with H  criterion in order to minimize the influence of the external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approach.

a b s t r a c tThis work concerns the tracking problem of uncertain Takagi-Sugeno (T-S) continuous fuzzy model with external disturbances. The objective is to get a model reference based output feedback tracking control law. The control scheme is based on a PDC structure, a fuzzy observer and a H 1 performance to attenuate the external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key point of the proposed approaches is to achieve conditions under a LMI (linear matrix inequalities) formulation in the case of an uncertain and disturbed T-S fuzzy model. This formulation facilitates obtaining solutions through interior point optimization methods for some nonlinear output tracking control problems. Finally, a simulation is provided on the well-known inverted pendulum testbed to show the efficiency of the proposed approach.

a b s t r a c tAn alternative to inverse dynamics joint torques estimation in human stance is proposed. This alternative is based on unknown-input observers which allow real-time estimation of joint torques and angular velocities from measurements of the angular positions. To design the aforementioned observer, a nonlinear state-space dynamical descriptor model is proposed. The descriptor model is then written into the form of a Takagi-Sugeno (T-S) model, from which a T-S observer in the descriptor form is designed. Then, convergence of the estimation errors (in position, velocities and torques) is established using a quadratic Lyapunov function through LMI conditions. Finally, the proposed approach is successfully compared with commonly used inverse dynamics joint torques estimation.

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This work concerns robust static output feedback controller (SOFC) design for uncertain and disturbed Takagi-Sugeno (TS) systems using an H-infinity criterion. The main result is based on a descriptor formulation of the closed-loop dynamics. The proposed approach allows avoiding appearance of crossing terms between the controller's and the TS system's input matrices leading to easier LMI formulation than existing studies in the literature. Moreover, the proposed SOFC design conditions don't require any restrictions on the output equation and allow dealing with unmeasurable premise variables. Indeed, taking advantage of the uncertain TS modeling, nonlinearities associated to unmeasurable premises variables can be reported from the nominal part to the uncertainties. To provide LMIs of less conservatism, the results are conducted in the non-quadratic framework. Finally, two numerical examples and a benchmark of a crane system are proposed to illustrate the efficiency of the SOFC design methodology.

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