带约束分数阶正系统稳定性与镇定的判定和计算的一个新方法

A new method for judgment and computation of stability and stabilization of fractional order positive systems with constraints

研究带控制约束的连续分数阶线性系统稳定性与镇定问题。利用Metzler矩阵理论和线性系统稳定性理论,得到连续分数阶线性系统为正系统和渐进稳定的一个充要条件。然后将求解带控制约束的连续分数阶系统状态反馈控制问题转化为一类线性规划问题。通过求解线性规划得到满足所给约束条件的控制律,使得闭环系统保持稳定性与正性并且满足控制约束条件。最后通过数值实验验证所提出方法的正确性。

This paper dealt with the stability and stabilization of continuous fractional-order linear systems with control constraints.By using Metzler matrix theory and linear system stability theory,a sufficient and necessary condition for continuous fractional-order linear systems to be positive and asymptotically stable was firstly obtained.Then the problem of state feedback control for continuous fractional-order systems with control constraints was transformed into a linear programming problem.By solving the linear programming,the control law is satisfying the given constraint condition was obtained,which makes the closed-loop system stable and positive and satisfies the control constraint condition.Finally,the correctness of the proposed method was verified by numerical experiments.