Stability Analysis and H infinity Decentralized Control for Discrete-Time Nonlinear Large-Scale Systems via Fuzzy Control Approach

This paper is concerned with stability analysis and H_∞ decentralized control of discrete-time nonlinear large-scale systems via fuzzy control approach. Each of them consists J interconnected discrete-time nonlinear subsystems. First, the discrete-time nonlinear large-scale system is represented by an equivalent Takagi-Sugeno discrete-time fuzzy large scale model. Next, based on this fuzzy large-scale model, a sufficient condition on stability of the discrete-time nonlinear large-scale system is proposed. Furthermore, H_∞ disturbance attenuation performance is analyzed and a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the H_∞ disturbance attenuation performance is achieved and the stability of the discrete-time nonlinear large-scale systems is also guaranteed. All these results are characterized in terms of a linear matrix inequalities (LMIs), which can be solved efficiently in practice by convex programming technique. The design method is illustrated by application to the problem of balancing double-inverted pendulums system.