Analysis Of The Uncertainty For LTI Systems

The main content of this paper is to study the stability margin of uncertain systems.The uncertainty represented respectively by the additive/multiplicative perturbation, thecoprime factorization and the gap metric has been fully introduced. The relationbetween the gap metric and coprime factorization is also investigated. And the maximalperturbation stability margin is solved by these three methods. Theadditive/multiplicative uncertainty can be represented by the transfer function form,and it requires the perturbation plant and the nominal plant have the same number ofclosed right plane poles. The coprime factorization use the coprime factors of thenominal plant and the coprime factors of perturbation plant to acquire the the maximalperturbation stability margin. It doesn't require the nominal plant and perturbation planthave the same number of closed right plane poles, but this method is more concise. Themetric between the graph space of the nominal plant and the graph space of theperturbation plant is described by the Gap metric. This method can describe both themetric of the stable plants and the metric of the unstable plants. The maximalperturbation stability margin gives a specific index to the solution of optimal robustcontroller.The second content of this paper is to investigate the perturbation stability marginof the perturbation plant controlled by the fixed controller. The solution of theperturbation stability margin of the fixed controller is presented when the uncertaintyrepresented respectively by the additive/multiplicative perturbation, the coprimefactorization. And the different methods are compared. This can be applied into practice.When the controller is designed, namely when the controller is fixed, the parameters ofcontroller needn't be adjusted if the perturbation have not surpass the perturbationstability margin of the fixed controller.Last,the simulation experiments have demonstrated the validity and practicabilityof the conclusion of this paper.