This paper addresses an observer-design method only using data. Usually, the observer requires a mathematical model of a system for state prediction and observer gain calculation. As an alternative to the model-based prediction, the proposed predictor calculates the states using a linear combination of the given data. To design the observer gain, the data which represent dual systems are derived from the data which represent the original system. Linear matrix inequalities that depend on data of the dual system provides the observer gains.

This paper presents the stability analysis for continuous-time Takagi-Sugeno fuzzy systems using a fuzzy Lyapunov function. The proposed fuzzy Lyapunov function involves the time derivatives of states to include new free matrices in the LMI stability conditions. These free matrices extend the solution space for Linear Matrix Inequalities (LMIs) problems. Numerical examples illustrate the effectiveness of the proposed methods.

The robust reduced order observer for a class of discrete-time Lipschitz nonlinear systems with external disturbance is proposed. It is shown that the proposed observer design can suppress the effect on the estimation error of external disturbance up to the prescribed level. Also, linear matrix inequalities are used to represent sufficient conditions on the existence of the proposed observer. Moreover, the maximum admissible Lipschitz constant of the proposed design is obtained for a given disturbance attenuation level. Finally, an illustrative example is given to verify the effectiveness of the proposed design.

A new deadbeat control scheme for linear systems with input constraints is presented. Input constraints exist in most control systems, but in conventional dead-beat control, logical strategy to handle it has not been studied enough. The proposed controller in this paper adjusts the number of steps for dead-beat tracking on-line, in order to achieve delayed deadbeat-tracking performance and satisfy any admissible input constraint. Increasing the number of steps for dead-beat tracking and formulating the corresponding degree of freedom into null-space vectors make it possible to obtain delayed dead-beat tracking, and minimize the inevitable delay, respectively. LMI feasibility problems are solved to numerically obtain the solution and minimize the unavoidable step-delay. As a result, calculation effort is reduced compared to LMI-optimization problem. The proposed schemes can be readily numerically implemented. Its practical usefulness is validated by simulation for 6-axis robot model and experimental results for DC-motor servoing.

This paper presents a robust reduced order observer for a class of Lipschitz nonlinear systems with external disturbance. Sufficient conditions on the existence of the proposed observer are characterized by linear matrix inequalities. It is also shown that the proposed observer design can reduce the effect on the estimation error of external disturbance up to the prescribed level. Finally, a numerical example is provided to verify the proposed design method.

This paper presents a deadbeat control scheme for linear systems with state constraints. The proposed controller increases the number of steps on-line for the deadbeat tracking performance, satisfying given admissible state constraints. LMI conditions are given to minimize the unavoidable step delay. The proposed schemes can be easily developed by using LMI approach, and are validated by numerical simulation.

A new control scheme is proposed to improve the system performance for discrete-time fuzzy systems by tuning control grade functions using neural networks. According to a systematic method of constructing the exact Takagi-Sugeno (T-S) fuzzy model, the system uncertainty is considered to affect the membership functions. Then, the grade functions, resulting from the membership functions of the control rules, are tuned by a back-propagation network. On the other hand, the feedback gains of the control rules are determined by solving a set of LMIs which satisfy sufficient conditions of the closed-loop stability. As a result, both stability guarantee and better performance are concluded. The scheme applied to a truck-trailer system is verified by satisfactory simulation results.