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研究了一类生物经济系统的稳定性问题,当生态系统中的某个生物量具有经济价值的时候,通过广义系统的描述将使得实际发生的现象和系统模型更加吻合。在一个具有普通意义的生物经济系统模型基础上,以离散的时滞广义系统作为研究对象,通过构造一个新的李亚普诺夫泛函并结合时滞分解的方法,得到了基于线性矩阵不等式形式的系统正则、因果且渐近稳定的判据。所得到的判据不再受时滞数值的具体约束,相应地扩大了判据的适用范围,具体的数值实例也显示了结果的有效性和较小的保守性。
The stability problem of a kind of bioeconomy system is studied. When a biomass in an ecosystem has economic value, the description of the generalized system will make the actual phenomenon more in line with the system model. On the basis of a generalized model of bioeconomy system, a discrete time-delay singular system is taken as the research object. By constructing a new Lyapunov functional and combining with the method of time-delay decomposition, System regular, causal and asymptotic stability criteria. The obtained criterion is no longer constrained by the time lag number, and the applicable scope of the criterion is extended accordingly. The numerical examples also show the validity and the conservativeness of the results.