This paper proposes a discrete version of a previous work of the authors in which an observer design for nonlinear systems based on the fuzzy polynomial (Taylor series) representation is discussed. The methodology provides single or fuzzy observer gains which are polynomial in the output and in the estimated states, if state and error (initially) lie in some operation regions. Then, some bounds on the error can be proved.

 This paper presents a new methodology for tuning the gains of fuzzy proportional-integral controllers where the closed loop system performance is explicitly taken into account. The gains are found by solving a nonlinear constrained optimization problem considering the systems dynamics described by a nonlinear model, and including a set of constraints on gains, control actions and on the system outputs. Experimental results ilustrate the relevance of using the proposed tuning technique.

 This paper focuses on $H_{infty}$ control design problem for T-S fuzzy time-delay systems with actuator saturation. Based on Lyapunov-Krasovskii Functional (LKF) combining the introduction of relaxed matrices, a $H_{infty}$ controller design method is presented in Linear Matrix Inequality (LMI) formal. The controller designed is capable to reject the disturbance assumed known and norm bounded. A numerical example is provided to verify the effectiveness of the proposed results.

 This paper introduces a fuzzy observer-based control approach for the vehicle lateral dynamics. The Takagi-Sugeno (TS) fuzzy model is utilized to describe the dynamics of a nonlinear time-varying lateral system. Based on the fuzzy model, a fuzzy observer is developed to estimate the side slip angle using the yaw velocity measurement. The objective of this study is twofold: first, the observer-based controller is designed to improve the stability of the vehicle although perturbations related to the nonlinearities of the contact force models, the variations of the adherence coefficients, etc. Second, the proposed strategy takes into account the unmeasurable membership functions of the TS formulation in the design of the observer.

 This paper addresses PID controller design using local model networks. The proposed method uses a common quadratic Lyapunov function to guarantee stability of the closed loop. To solve the resulting bilinear matrix inequalities (BMI) an iterative procedure is introduced which is based on state of the art linear matrix inequalities solvers (iLMI). Due to the fact that the Lyapunov approach requires a state-space model a suitable closed-loop state-space system is introduced. An example demonstrates the effectiveness of the proposed method.

 This paper proposes a new approach of observer design for nonlinear systems described by a Takagi-Sugeno model. Its main contribution concerns models with premise variables depending on the system states which are completely or partially unknown. This case is more difficult than when the premise variables are known or measured. Indeed, in this case, weighting functions of the observer depend on state estimates and the state estimation error is then governed by a Lipschitz nonlinear system. Here, two main results are established. Firstly, relaxed stability conditions are provided, using a nonquadratic Lyapunov function, to guarantee asymptotic stability of the observer. This aims to reduce the conservativeness compared to the existing works and enhance the maximal admissible Lipschitz constant for which the linear matrix inequality (LMI) conditions are feasible. Secondly, the Input-to-State Stability concept combined to a nonquadratic Lyapunov function are used to guarantee a bounded state estimation error which relaxes the conservativeness related to the Lipschitz constant. The robustness aspect is dealt with respect to some bounded modeling uncertainties and additive bounded perturbations. The stability conditions are expressed in terms of LMI.