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Although the cyber-physical system stability is widely studied, scholars focus more on system stability with communication time delay. Therein, grid-connected inverters with the digital control system are regarded as one simplest and typical cyber-physical system. Meanwhile, the switching/sampling frequency of the inverter is always selected as low as possible from an efficiency viewpoint, resulting in unavoidable delay time. This delay time is apt to cause the system instability, which is more prone to severity under weak grid. To this end, this paper provides a minimum switching/sampling frequency for grid-connected inverters. Firstly, the system impedance model with equivalent delay time is constructed, which is based on padé approximate approach. This equivalent delay time consists of three parts, i.e., sampling delay time in cyber/physical level, calculation delay time in cyber level and pulsewidth modulation delay time in physical level, which reflects the cyber-physical interaction impact. Furthermore, the stability forbidden criterion is applied to make the switching/sampling frequency solving process become Hurwitz matrix identification problem through space mappings. Based on these space mappings, an adaptive step search approach is adopted to obtain the minimum switching/sampling frequency. Finally, the proposed approach can well evaluate the system stability under different frequencies through simulation and experiment. [ABSTRACT FROM AUTHOR]

In this article, the issue of almost output regulation for continuous-time switched positive systems is investigated. We take into consideration the different coordinates transformations in which the subsystems are switched corresponding to the individual coordinate system. A new design scheme is firstly proposed in this manner. Furthermore, each group of the regulator equations has its own solution. Two types of control strategies, including a state feedback law and an error feedback law, are adopted. In contrast to the nominal output regulation problem, we consider the case where an unknown external disturbance affects the systems and the exogenous systems. Therefore, a concept of the almost output regulation for the considered systems is proposed. Then, all tractable conditions guaranteeing the solvability of the addressed problem are presented in terms of linear matrix equalities as well as linear vector inequalities by means of the constructed multiple linear copositive Lyapunov functions. A positive circuit is finally used to illustrate the applicability and availability of the developed theoretical findings. [ABSTRACT FROM AUTHOR]