Robust Control for Uncertain Fuzzy Nonlinear Time-Delay Systems with Application to Practical Systems

点击翻译按钮获取中文摘要

In this research project, system analysis and synthesis of Takagi-Sugeno fuzzy systems with time-delay and uncertainties were concerned. First, stability analysis on a nominal fuzzy system with time-invariant delay was considered. In general, it is difficult to obtain a necessary and sufficient stability condition for the system because a system under consideration is a nonlinear time-delay system. Hence, an original nonlinear time-delay system was transformed into a fuzzy time-delay system and a stability condition for a fuzzy time-delay system was obtained as a sufficient condition via linear matrix inequality. In the derivation of stability condition, Leibniz-Newton formula and free weighting matrix method were employed to reduce the conservatism in stability condition. A stability condition was extended to a robust stability condition for a fuzzy time-delay system with uncertainties in system matrices. Based on such stability conditions, stabilizing controller for a nominal fuzzy time-delay system and robust stabilizing controller for an uncertain fuzzy time-delay system were designed. As for a class of systems, not only systems with discrete delays but also systems with discrete and distributed delay are concerned. As for time delays, not only time-invariant delays but also time-varying delays were considered. Moreover, an Hoc controller design which attenuate system disturbances and measurement noises was proposed. An Hoc filter which plays an important role in control design for a fuzzy time-delay system was also given. Finally, the above theoretical design was applied to practical systems. After making numerical simulations, controllers designed as above were applied to practical systems such as inverted pendulum and helicopter. It was found that such controllers worked well for those practical systems.