基于区间数学的系统稳定性分析

Analysis of System Stability Based on Interval Mathematics

根据Routh判据,区间数学模型的线性系统稳定性的充要条件是第一列全部为正数,等价于其下界大于零。如果第一列区间数以零为下界,则特征方程有成对虚根,系统临界稳定。而Nyquist稳定判据则根据系统的开环频率特性判断闭环系统稳定性。由于参数可行域的引入,等价于给了系统一定的稳定裕度。

According to the Routh criterion, the linear interval mathematical model system stability＇s necessary and sufficient conditions are the first row numbers and are all positive numbers; they equal to its lower bound over zero. If the first row interval numbers take zero as a Lower bound, then the character equation has pairs of conjugated imaginary radixes, and the system is in critical stability. The Nyquist stability criterion judges the closed-loop systems＇ stability, according to the system＇s open-loop frequency characteristic. And the introduction of parameter feasible regions＇ equals to give the system a certain stability margin.