Abstract-Unnecessary communication and computation in the periodic execution of control tasks lead to over-provisioning in hardware design (or underexploitation in hardware utilization) in control applications, such as networked control systems. To address these issues, researchers have proposed a new class of strategies, named event-driven strategies. Despite of their beneficiary effects, matters like task scheduling and appropriate dimensioning of communication components have become more complicated with respect to traditional periodic strategies. In this paper, we present a formal approach to derive an abstracted system that captures the sampling behavior of a family of eventtriggered strategies for the case of LTI systems. This structure approximately simulates the sampling behavior of the aperiodic control system. Furthermore, the resulting quotient system is equivalent to a timed automaton. In the construction of the abstraction, the state space is confined to a finite number of convex regions, each of which represents a mode in the quotient system. An LMI-based technique is deployed to derive a sampling time interval associated to each region. Finally, reachability analysis is leveraged to find the transitions of the quotient system.

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Treating optimization methods as dynamical systems can be traced back centuries ago in order to comprehend the notions and behaviors of optimization methods. Lately, this mind set has become the driving force to design new optimization methods. Inspired by the recent dynamical system viewpoint of Nesterov's fast method, we propose two classes of fast methods, formulated as hybrid control systems, to obtain prespecified exponential convergence rate. Alternative to the existing fast methods which are parametric-in-time second order differential equations, we dynamically synthesize feedback controls in a state-dependent manner. Namely, in the first class the damping term is viewed as the control input, while in the second class the amplitude with which the gradient of the objective function impacts the dynamics serves as the controller. The objective function requires to satisfy the so-called Polyak-Lojasiewicz inequality which effectively implies no local optima and a certain gradient-domination property. Moreover, we establish that both hybrid structures possess Zeno-free solution trajectories. We finally provide a mechanism to determine the discretization step size to attain an exponential convergence rate.

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