分数阶时变切换系统有限时间异步控制

Finite Time Asynchronous Control of Fractional Order Time-varying Switched Systems

针对一类时变切换系统,当考虑子系统具有分数阶(Fractional Order)特性时,提出了一种基于模型依赖平均驻留时间方法的有限时间稳定性条件及异步切换控制策略.借助Caputo分数阶导数引理和切换Lyapunov函数,利用矩阵不等式技术提出了分数阶时变切换系统有限时间稳定的充分条件.将有限时间稳定的结果进一步推广到有限时间有界的情形,利用平均驻留时间思想提出了分数阶时变切换系统有限时间有界的充分条件,基于该条件设计了系统的异步切换控制器.所给出的设计方法将系统异步切换控制问题转化为矩阵不等式组的求解问题.通过数值仿真验证了所提控制方法的有效性.

For a class of time-varying switched systems,when considering the fractional order characteristics of subsystems,finite time stability condition and asynchronous switching control strategy are proposed based on model dependent average dwell time method.With the help of Caputo fractional derivative lemma and switched Lyapunov function,a sufficient condition for the finite time stability of fractional time-varying switched systems is proposed by using matrix inequality technology and the result of finite time stability is further extended to the case of finite time boundedness.A sufficient condition for finite time boundedness of fractional order time-varying switched systems is proposed using the idea of average dwell time and the asynchronous switching controller of the system is designed based on this condition.The proposed design method transforms the asynchronous switching control problem into the solution of matrix inequalities.The effectiveness of the proposed control method is verified by numerical simulation.