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This work studies the performance of an event-based control approach, namelylevel-triggered sampling, in a standard multidimensional single-integratorsetup. We falsify a conjecture from the literature that the deployed $p$-normin the triggering condition supposedly has no impact on the performance of thesampling scheme in that setting. In particular, we show for the consideredsetup that the usage of the maximum norm instead of the Euclidean norm inducesa performance deterioration of level-triggered sampling for sufficiently largesystem dimensions, when compared to periodic control at the same sampling rate.Moreover, we investigate the performance for other $p$-norms in simulation andobserve that it degrades with increasing $p$. In addition, our findings revealthe previously unknown role of the triggering rule in the cause of a recentlydiscovered phenomenon: Previous work has shown for a single-integratorconsensus setup that the commonly observed performance advantage of event-basedcontrol over periodic control can be lost in distributed settings with acooperative control goal. In our work, we obtain similar results for anon-cooperative setting only by adjusting the norm in the level-triggeredsampling scheme. We therefore demonstrate that the performance degradationfound in the distributed setting originates from the triggering rule and notfrom the considered cooperative control goal.

Performance implications of different $p$-norms in level-triggered sampling