The Study Of Robust Stability For Systems With Parametric Uncertainty

The stability is one of most concerned problem in the control systems. How-ever the parametric uncertainty can destroy the systems'stability and other per-formance. In order to maintain the system's stability and performance, the robustcontrol attempts to describe the object's uncertainty and synthesize its controllerwithin the perturbation scope permitted by uncertainty. So, the robust controltheory has been widely concerned and a lot of excellent results have been got incontrol field.This article mainly based on the model of system with bounded linear para-metric uncertainty. On the basis of recent literature using methods of matrixanalysis and robust inverse Nyquist array methods of multiple variable frequencytheorem, we study the variation of the system's transfer function matrix whenparametersΘare variate or uncertain. A new method of estimating the widthof the robust Gershgorin bands is proposed, improve and promote these previousconclusions. On the basis the robust stability theorem of system with parametricuncertainty is proposed. Based on this theorem the robust control design methodis derived for the system with multiple variable parametric uncertainty. Maincontents as follows:In chapter one, we first present some background knowledge and recentworks for system with parametric uncertainty. Then we introduce the mathe-matic model of system with parametric uncertainty, as well as propose the statusquo of which is the main work.In chapter two, uses location of matrix eigenvalues theorem and applyingsome techniques of inequalities, we acquire several robust Gershgorin theorem.Based on this theorem, the definition of robust diagonal dominance and robustGershgorin bands are proposed, as well as uses the related information of thetransfer function matrix's element the estimation method is derived for the Ger-shgorin bands, improve these previous conclusions and reduce conservation. Andillustrate the e?ectiveness of method by an example.In chapter three, uses the conclusion of chapter two, analysis the robuststability of system with parametric uncertainty, propose the theorem of robuststability. Then based on this theorem the robust control design method is de-rived for the system with multiple variable parametric uncertainty. To simulate a group of industrial model, the results illustrates the e?ectiveness and superiorityof this design method.