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Feedback control laws have been traditionally implemented in a periodic fashion on digital hardware. Although periodicity simplifies the analysis of the mismatch between the control design and its digital implementation, it also leads to conservative usage of resources such as CPU utilization in the case of embedded control. We present a novel technique that abandons the periodicity assumption by using the current state of the plant to decide the next time instant in which the state should be measured, the control law computed, and the actuators updated. This technique, termed self-triggered control, is developed for two classes of nonlinear control systems, namely, state-dependent homogeneous systems and polynomial systems. The wide applicability of the proposed results is illustrated in two well known physical examples: a jet engine compressor and the rigid body.

Event-triggered control consists of closing the feedback loop whenever a predefined state-dependent criterion is satisfied. This paradigm is especially well suited for embedded systems and networked control systems since it is able to reduce the amount of communication and computation resources needed for control, compared to the traditional periodic implementation. In this paper, we propose a framework for the event-triggered stabilization of nonlinear systems using hybrid systems tools, that is general enough to encompass most of the existing eventtriggered control techniques, which we revisit and generalize. We also derive two new event-triggering conditions which may further enlarge the inter-event times compared to the available policies in the literature as illustrated by two physical examples. These novel techniques exemplify the relevance of introducing additional variables for the design of the triggering law. The proposed approach as well as the new event-triggering strategies are flexible and we believe that they can be used to address other event-based control problems.

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An inevitable consequence of the global power system transition towards nearly 100% renewable-based generation is the loss of conventional bulk generation by synchronous machines, their inertia, and accompanying frequency and voltage control mechanisms. This gradual transformation of the power system to a low-inertia system leads to critical challenges in maintaining system stability. Novel control techniques for converters, so-called grid-forming strategies, are expected to address these challenges and replicate functionalities that so far have been provided by synchronous machines. This article presents a low-inertia case study that includes synchronous machines and converters controlled under various grid-forming techniques. In this work 1) the positive impact of the grid-forming converters on the frequency stability of synchronous machines is highlighted, 2) a qualitative analysis which provides insights into the frequency stability of the system is presented, 3) we explore the behavior of the grid-forming controls when imposing the converter dc and ac current limitations, 4) the importance of the dc dynamics in grid-forming control design as well as the critical need for an effective ac current limitation scheme are reported, and lastly 5) we analyze how and when the interaction between the fast gridforming converter and the slow synchronous machine dynamics can contribute to the system instability.