Analysis And Application On A Class Of Uncertain Nonlinear Control Systems

The control of nonlinear systems is an attractive field in current control theory. Theresearch of nonlinear systems is more difficult and complex than linear systems because ofthe particular characteristics of nonlinear systems. So it is meaningful to do the research onnonlinear systems, especially the uncertain nonlinear systems.In this paper, we study on a class of uncertain nonlinear systems. Firstly, we use theT-S fuzzy model to represent the system and design its fuzzy state observer by using theauxiliary variables. We get that if the auxiliary variables satisfy given adaptive laws, thedesigned fuzzy state observer can estimate the states of the plant exactly. Secondly, wepropose a approach to design the fuzzy controller for the studied system base on thedesigned observer. By using the Lyapunov stability theory, we conclude the criteria ofstability for the closed-loop control system can be change into the problem that looking fora common symmetric positive definite matrix. Then, we present a method to find thiscommon symmetric positive definite matrix by using the theory of Lie algebra. Thirdly, weanalysis the structure of a set of system matrices and their disturbance matrices for theregular stable systems. We give a necessary and sufficient condition for their structure.Similar to the regular systems, we also get the structure for the admissible generalizedsystems. Finally the proposed schemes is applied to the M730magnetic levitation which isa Single Input Single Output uncertain nonlinear system and do the simulation. The resultof the simulation is in line with expectations which show the correctness and effectives forthe scheme of designing the fuzzy state observer and fuzzy controller.