Modeling and controller design for complex flexible nonlinear systems via a fuzzy singularly perturbed approach

This paper investigates the problems of modeling and controller design for complex flexible nonlinear systems (CFNSs) based on a fuzzy singularly perturbed model. A standard discrete-time fuzzy singularly perturbed model (FSPM) is firstly constructed to estimate CFNSs. Based on a matrix spectral norm approach, a static output feedback controller is designed, which guarantees the resulting closed-loop system is asymptotically stable. The gains of controllers are obtained by solving a set of ε-independent linear matrix inequalities (LMIs) so the ill-conditioned problems caused by ε can be easily avoided. Finally, the proposed approach is applied to modeling and attitude control of flexible satellites. In contrast to the existing results, the proposed method has the following advantages: (i) flexible vibrations can be effectively suppressed, and (ii) the control performance is greatly improved, as well as (iii) the control inputs do not need to be limited in controller design. Two practical examples are provided to illustrate the effectiveness of the presented approach. From the simulation results, it can be seen that the proposed approach can also effectively overcome the external disturbances and noises.