This paper investigates the optimization problem for a class of switched interconnected positive linear systems (SIPLSs), of which each subsystem is composed of several positive interconnected components. Both the continuous-time and periodic sampling control schemes are considered. Combining with the characteristics of the interconnection and positivity, a novel class of multiple co-positive Lyapunov functions is constructed. Based on the multiple Lyapunov functions method, a state-dependent switching law with a dwell time constraint is introduced so that the state is continuously evaluated after the dwell time. Furthermore, the designed switching law is extended to a new sample-based scenario where the state is periodically evaluated after the dwell time. In both cases, suitable cost functions are selected to estimate the performance of the SIPLSs, and the upper bounds are calculated. Finally, numerical examples are considered to illustrate the effectiveness of the presented results.

中文翻译：

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带驻留时间的状态相关切换下切换互连正系统的优化

本文研究了一类交换互连正线性系统（SIPLS）的优化问题，其中每个子系统由几个正互连组件组成。连续时间和周期性采样控制方案都被考虑。结合相互关联性和正性的特点，构造了一类新的多重共正李雅普诺夫函数。基于多李雅普诺夫函数方法，引入了具有驻留时间约束的状态相关切换律，以便在驻留时间后连续评估状态。此外，设计的切换定律扩展到一个新的基于样本的场景，其中在停留时间后定期评估状态。在这两种情况下，选择合适的成本函数来估计 SIPLS 的性能，并计算上限。最后，考虑数值例子来说明所呈现结果的有效性。