Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays
Exponential Stability of Homogeneous Positive Systems of Degree One With Time-Varying Delays
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DOI：
10.1109/tac.2013.2292739
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发表时间：
2013-11
影响因子：
6.8
通讯作者：
Hamid Reza Feyzmahdavian;Themistoklis Charalambous;M. Johansson
中科院分区：
文献类型：
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作者：
Hamid Reza Feyzmahdavian;Themistoklis Charalambous;M. Johansson
虽然存在有界时滞的正线性系统的渐近稳定性已经得到了深入的研究，但非线性正系统的理论还相当不成熟。本技术说明给出了一组条件，用于建立时滞无关稳定性和限制一类重要的非线性正系统的衰减率，其中包括正线性系统作为特例。具体地说，当时滞有一个已知的上界时，我们得到了：a）连续时间正系统，其向量场是齐次的和合作的; B）离散时间正系统，其向量场是齐次的和保序的指数稳定的充分必要条件.然后，我们提出了明确的表达式，使我们能够量化延迟对衰减率的影响，并表明，我们的边界提供的正线性系统的最佳衰减率可以通过凸优化。最后，我们将结果推广到一般的线性时变时滞系统。
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This technical note presents a set of conditions for establishing delay-independent stability and bounding the decay rate of a significant class of nonlinear positive systems which includes positive linear systems as a special case. Specifically, when the time delays have a known upper bound, we derive necessary and sufficient conditions for exponential stability of: a) continuous-time positive systems whose vector fields are homogeneous and cooperative and b) discrete-time positive systems whose vector fields are homogeneous and order-preserving. We then present explicit expressions that allow us to quantify the impact of delays on the decay rate and show that the best decay rate of positive linear systems that our bounds provide can be found via convex optimization. Finally, we extend the results to general linear systems with time-varying delays.