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In this paper, we consider the modeling and (robust) control of a DC-DC boost converter. In particular, we derive a mathematical model consisting of a constrained switched differential inclusion that includes all possible modes of operation of the converter. The obtained model is carefully selected to be amenable for the study of various important robustness properties. For this model, we design a control algorithm that induces robust, global asymptotic stability of a desired output voltage value. The guaranteed robustness properties ensure proper operation of the converter in the presence of noise in the state, unmodeled dynamics, and spatial regularization to reduce the high rate of switching. The establishment of these properties is enabled by recent tools for the study of robust stability in hybrid systems. Simulations illustrating the main results are included.

This paper proposes a general framework for analyzing continuous-time systems controlled by event-triggered algorithms. Closed-loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event-triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions and studied using recently developed tools for robust stability. Properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated in several event-triggered strategies available in the literature.

In this paper, we analyze the properties of the vector fields associated with all possible configurations of a single-phase DC/AC inverter with the objective of designing a hybrid controller for the generation of an approximation of a sinusoidal reference signal. Using forward invariance tools for general hybrid systems, a hybrid controller is designed for the switched differential equations capturing the dynamics of the DC/AC inverter. Then, global asymptotic stability of a set of points nearby the reference trajectory, called the tracking band, is established. This property is found to be robust to small perturbations, and variation of the input voltage. Simulations illustrating the major results are included.

Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with statedepending conditions enabling flows and jumps is studied. Several notions of forward invariance are considered and sufficient conditions in terms of the objects defining the system are introduced. In particular, we study forward invariance notions that apply to systems with nonlinear dynamics for which not every solution is unique or may exist for arbitrary long hybrid time. Such behavior is very common in hybrid systems. Lyapunov-based conditions are also proposed for the estimation of invariant sets. Applications and examples are given to illustrate the results. In particular, the results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence of solutions.