School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China.
Department of Nutrition, Shandong Provincial Hospital affiliated to Shandong University, Jinan 250021, China; Department of Biostatistics, School of Public Health, Shandong University, Jinan 250012, China.
ISA Trans. 2019 Oct;93:55-69. doi: 10.1016/j.isatra.2019.03.020. Epub 2019 Mar 28.
This paper addresses the problems of robust stability analysis and L-gain controller synthesis for uncertain impulsive positive systems. First, by employing the idea of impulse interval partitioning, an impulse-time-dependent discretized copositive Lyapunov function is proposed to analyze the robust stability and L-gain performance of the considered system without control inputs, and several stability conditions and L-gain criteria are respectively derived. Subsequently, a sufficient condition is formulated for the existence of state-feedback controllers with which not only the positivity and robust uniform asymptotic stability of the resulting closed-loop system are guaranteed, but also a prescribed L-gain performance is satisfied simultaneously. Furthermore, to make the controller synthesis problem numerically tractable, we propose an iterative convex optimization algorithm to compute the desired controller parameters. Finally, three numerical examples and two realistic examples are presented to show the effectiveness and applicability of the proposed methodology.
本文针对不确定脉冲正系统的鲁棒稳定性分析和 L-增益控制器综合问题进行了研究。首先，通过采用脉冲区间划分的思想，提出了一个脉冲时变离散共正定 Lyapunov 函数，用于分析无控制输入时所考虑系统的鲁棒稳定性和 L-增益性能，并分别推导出了几个稳定性条件和 L-增益准则。随后，给出了存在状态反馈控制器的充分条件，使得所得到的闭环系统不仅具有正实性和鲁棒一致渐近稳定性，而且同时满足给定的 L-增益性能。此外，为了使控制器综合问题具有数值可处理性，我们提出了一种迭代凸优化算法来计算所需的控制器参数。最后，通过三个数值实例和两个实际实例验证了所提出方法的有效性和适用性。
