Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension

The robust adaptive fuzzy control problem is investigated for a single machine bus system with static var compensator (SVC). This design does not require that speed of the generator rotor and susceptance of the overall system are measured, and also does not require that the parameters of controlled system are known accurately. The fuzzy logic systems are used to approximate the nonlinear functions of the system, and a fuzzy state observer is designed to estimate the speed of the generator rotor and susceptance. By utilizing the fuzzy state observer, and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the angle of the generator rotor follows a desired value. Simulation results are presented to show the effectiveness of the approach.