With The Robustness Analysis And Synthesis Of Polytopic Uncertain Systems

Uncertain systems have received much attention in recent years,since its significant applications in engineering.There's much research on systems,with structured uncertainty. However,there're few studies on systems with polytopic uncertainty.Based on parameter dependent Lyapunov function and quadratic stability theory,this paper studies the problem of robust analysis and synthesis for continuous-time systems as well as discrete-time systems with polytopic uncertainty,respectively.The main results obtained in this paper are as follows:1,Concerning the continuous systems with polytopic uncertainty,firstly,a new robust stability condition is proposed by means of LMI.Then based on the preceding condition,the problem of robust stabilization is considered.The sufficient stabilization conditions are formulated in terms of a set of linear matrix inequalities.Furthermore,the condition for robust H_∞control is presented.A state feedback controller is designed such that the closed-loop system is not only robustly stable but also with a prescribed H_∞performance level.2,About the discrete-time systems with polytopic uncertainty,firstly,the problem of parameter independent and parameter dependent state feedback controller designs are addressed.The robust stabilization conditions are presented,respectively.Secondly,the conditions for robust H₂ and H_∞control are presented respectively.A state feedback controller is designed such that the closed-loop system is not only robustly stable but also with a prescribed H₂ or H_∞performance level.These conditions above are formulated in terms of a set of linear matrix inequalities involving only the vertices of the polytope domain.So they can be solved by LMI toolbox in Matlab.Finally,some numerical examples are given to illustrate the improvement over existing results.