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We derive necessary and sufficient conditions for stability analysis of a positive feedback interconnection of a discrete-time negative imaginary system and a discrete-time strictly negative imaginary system. General stability analysis results for continuous-time negative imaginary systems connected in positive feedback have recently been proposed. Those recent results extend previous theorems by removing restrictive assumptions on the infinite frequency gains imposed in the earlier literature and by extending the class of negative imaginary systems for which the results are applicable to include systems with free body dynamics (i.e., poles at the origin). Here, we present the discrete-time counterparts of the aforementioned recently developed results which specialise to simple and easy-to-check conditions under specific assumptions. Last, we illustrate some of the results by several examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper develops robust control and power management strategies for a 6 kW stationary proton exchange membrane fuel cell (PEMFC) hybrid power system. The system consists of two 3 kW PEMFC modules, a Li–Fe battery set, and electrical components to form a parallel hybrid power system that is designed to supply uninterruptible power to telecom base stations during power outages. The study comprises three parts: PEMFC control, power management, and system integration. First, we apply robust control to regulate the hydrogen flow rates of the PEMFC modules in order to improve system stability, performance, and efficiency. Second, we design a parallel power train that consists of two PEMFC modules and one Li–Fe battery set for the uninterruptible power supply (UPS) requirement. Lastly, we integrate the system for experimental verification. Based on the results, the proposed robust control and power management are deemed effective at improving the stability, performance, and efficiency of the stationary power system. [Copyright &y& Elsevier]