The Study On The Domains Of Practical Stability Of A Kind Of Dynamical System And The Application In Electricity Market

Stability theory is concerned with the state of differential equation when time approach infinity. Not only in research,the stability plays an important role,but also in natural science,engineering, environment and socio-economic,it has broad application.Following results are obtained:Firstly,we introduce the related knowledge of practical stability domain,the estimate of practical stability domain and the estimates of practical stability domain with settling timeτ_s.Secondly,by Lyapunov method and inequalities,the estimate of practical stability domains on a kind of non-linear dynamical system and the estimate of practical stability domains on a kind of non-linear time delay system was studied,and the way to construct the estimate of practical stability domains of a system was given.Thirdly,by Lyapunov function,discussed the practical stability domains on a kind of discrete equation and the practical stability domains on a kind of discrete equation with time delay.The conditions is easy and convenient,and improved the results in the proceeding literature.At last,the stability of electricity market model was discussed in the base of theories.