【摘要】 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。更多还原

【Abstract】 This paper studies the problem of the stability analysis for a class of bio-economic systems.When a biomass in the ecological systems has an economic value,the description via the singular systems makes the actual occurrence and system model more consistent.Based on the model of a bio-economic system in the ordinary sense,by regarding discrete-time singular systems with delays as the research object and constructing a new Lyapunov functional combined with the time delay decomposition method,a regular,causal and asymptotic stability criterion is obtained in terms of linear matrix inequalities(LMIs).The proposed criterion is no longer subject to specific constraints of delay values,so the applicable range of the criterion is correspondingly expanded.A numerical example is also given to show the effectiveness and less conservative of the results.更多还原