Phase limitations of Zames-Falb multipliers

Phase limitations of both continuous-time and discrete-time Zames-Falb multipliers and their relation with the Kalman conjecture are analysed. A phase limitation for continuous-time multipliers given by Megretski is generalised and its applicability is clarified; its relation to the Kalman conjecture is illustrated with a classical example from the literature. It is demonstrated that there exist fourth-order plants where the existence of a suitable Zames-Falb multiplier can be discarded and for which simulations show unstable behavior. A novel phase-limitation for discrete-time Zames-Falb multipliers is developed. Its application is demonstrated with a second-order counterexample to the Kalman conjecture. Finally, the discrete-time limitation is used to show that there can be no direct counterpart of the off-axis circle criterion in the discrete-time domain

Reconciling the influence of task-set switching and motor inhibition processes on stop signal after-effects.

Executive response functions can be affected by preceding events, even if they are no longer associated with the current task at hand. For example, studies utilizing the stop signal task have reported slower response times to "GO" stimuli when the preceding trial involved the presentation of a "STOP" signal. However, the neural mechanisms that underlie this behavioral after-effect are unclear. To address this, behavioral and electroencephalography (EEG) measures were examined in 18 young adults (18-30 years) on "GO" trials following a previously "Successful Inhibition" trial (pSI), a previously "Failed Inhibition" trial (pFI), and a previous "GO" trial (pGO). Like previous research, slower response times were observed during both pSI and pFI trials (i.e., "GO" trials that were preceded by a successful and unsuccessful inhibition trial, respectively) compared to pGO trials (i.e., "GO" trials that were preceded by another "GO" trial). Interestingly, response time slowing was greater during pSI trials compared to pFI trials, suggesting executive control is influenced by both task set switching and persisting motor inhibition processes. Follow-up behavioral analyses indicated that these effects resulted from between-trial control adjustments rather than repetition priming effects. Analyses of inter-electrode coherence (IEC) and inter-trial coherence (ITC) indicated that both pSI and pFI trials showed greater phase synchrony during the inter-trial interval compared to pGO trials. Unlike the IEC findings, differential ITC was present within the beta and alpha frequency bands in line with the observed behavior (pSI > pFI > pGO), suggestive of more consistent phase synchrony involving motor inhibition processes during the ITI at a regional level. These findings suggest that between-trial control adjustments involved with task-set switching and motor inhibition processes influence subsequent performance, providing new insights into the dynamic nature of executive control