This paper introduces an H∞fuzzy control synthesis method for a nonlinear large-scale system with a reduced number of linear matrix inequalities (LMIs). It is well known that a nonlinear large-scale system can be transformed to a Takagi-Sugeno (T-S) fuzzy system by using “sector nonlinearity” or “local approximation in fuzzy partition spaces” methods. Next, in order to achieve the fuzzy control design for this T-S fuzzy system, we solve the stabilization conditions that are represented by the LMIs. However, if the number of LMIs is large, the control design process may become very complicated. In this study, based on the Lyapunov method and S-procedure, several theorems are proposed for the synthesis of parallel distributed compensation (PDC)-type fuzzy control such that the nonlinear large-scale system achieves H∞control performance, and the number of LMIs to be solved is reduced explicitly. As a result, the control design process will become much easier. Furthermore, if the modeling error between the nonlinear system and T-S fuzzy system exists, the robust H∞control performance and the number reduction of LMIs are also achieved by the proposed theorem. Several examples are presented in this paper to show the number reduction effect of LMIs and the effectiveness of the proposed controller synthesis.

In this paper, an energy-saving algorithm to achieve minimum energy consumption and high efficiency for a pumping system is proposed. In the first step, the mathematical model of the pumping system is given. In the second step, one optimal operating condition of pump system is obtained by the proposed energy-saving algorithm. Moreover, a fuzzy decision making is used to make the optimal decision of pumping system operation. Finally, an experimental result is presented to prove the efficiency of the algorithm.

This paper studies the stabilization problem of a kind of large-scale fuzzy system. The large-scale fuzzy system consists of a large number of nonlinear subsystems which are linked through time-varying interconnections. Furthermore, S-procedure is used to solve the transformation from non-LMI problem to LMI problem. Finally, a numerical simulation for a large-scale fuzzy system is given to show the applications of the present approach.

A stability analysis and controller synthesis methodology for an inverted robot arm system is proposed in this paper. This uncertain system is modeled by a state space Takagi-Sugeno (T-S) fuzzy model with linear nominal part and structure bounded parameter uncertainties in the state equations of each fuzzy rule. First, a sufficient condition on robust stability of the continuous perturbed time-delay affine T-S (CPTDATS) fuzzy models of inverted robot arm is proposed. Then, Hinfin-disturbance attenuation performance of the fuzzy models is analyzed. At last, a numerical example shows the use of the proposed approach on the stabilization and Hinfin-disturbance attenuation for the inverted robot arm systems.

A parallel distributed compensation (PDC) based fuzzy controller design issue to discrete time-delay affine Takagi-Sugeno (T-S) fuzzy systems is considered. It is noted that the discrete time-delay affine T-S fuzzy systems stabilization matrix inequalities belong to a class of bilinear matrix inequalities (BMI) and cannot be solved by a convex optimization algorithm. Due to this reason, an iterative linear matrix inequality (ILMI) algorithm is used to represent the BMI problem into a linear matrix inequality (LMI) problem and to obtain the feasible solution for the synthesis of the discrete time-delay affine T-S fuzzy systems. Finally, a numerical simulation is given to show the applications of the present approach.