切换正系统稳定性及l_(1)增益性能分析

Stability and l_(1)-gain performance analysis for switched positive systems

研究一类切换正系统,其中包括稳定及不稳定子系统,分别将其运行区间看作τ部分与T部分,建立持续驻留时间切换正系统模型.基于此,结合多余正Lyapunov函数方法建立系统稳定性判据并获得持续驻留时间具体数值,降低已有平均驻留时间结果的保守性.此外,在持续驻留时间切换条件下通过累积计算每个阶段切换次数上限的方法,进一步分析切换正系统的l_(1)增益性能并计算出l_(1)增益.所获得条件均为标准线性规划形式,方便在Matlab中利用Linprog函数求解.最后,通过数值仿真验证了所提方法的可行性.

A class of switched positive systems including stable and unstable subsystems are studied.The operation intervals of stable and unstable subsystems are regarded asτ-portion and T-portion respectively,then the switched positive systems model with persistent dwell time switching can be established.On this basis,by using the multiple co-positive Lyapunov functions method,the stability criterion is established and the specific value of persistent dwell time is calculated.Compared to the existing results based on average dwell time method,the conservatism is reduced.Furthermore,under the condition of persistent dwell time switching,the l_(1)-gain performance of switched positive system is analyzed and the l_(1)-gain is obtained by cumulatively calculating the upper limit of number of switches in each stage.All the above conditions are in the form of standard linear programming,which is convenient to solve by using Linprog function in Matlab.Finally,numerical simulation is presented to verify the feasibility of the proposed method.