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In this paper, tools to study forward invariance properties with robustness to disturbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of differential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without disturbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout this paper to illustrate the main ideas.

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.

Forward invariance with robustness to disturbances for hybrid dynamical systems modeled by hybrid inclusions with state-dependent conditions enabling flows and jumps is studied. In particular, we study forward invariance notions that apply to systems with hybrid inputs and disturbances with nonlinear dynamics, for which not every solution is unique or may exist for arbitrary long hybrid time. Given state-feedback laws, notions of robust forward invariance of sets for closed-loop system are introduced. Sufficient conditions in terms of the objects defining the system are presented. One result using Lyapunov-based conditions removes the usual Lipschitz constraint on continuous dynamics. A bouncing ball example is given to illustrate major results.

Early vocabularies in most languages tend to contain more nouns than verbs. Yet, the strength of this noun bias hasbeen observed to vary across languages and cultures. Two main hypotheses have aimed at explaining such variations; eitherthat the relative importance of nouns vs. verbs is language- specific, or that socio-cultural influences shape early vocabularystructures. The present study compares the relative distribution of verbs and nouns, in English, between two groups of bilingualinfants and toddlers; Malay-English and Mandarin- English. We found that early English lexicons of Mandarin- Englishbilinguals contained more verbs than in the English lexicon of Malay-English bilinguals, in both comprehension and production.We discuss the potential role of socio-cultural influences on the vocabulary structure in young users of a language.

We present results for forward invariance-based control of hybrid dynamical systems via static feedback. Using recent results on forward invariance for hybrid systems without inputs, we present conditions on the state-feedback laws to induce forward invariance of a set for hybrid systems with inputs. In addition, we propose a notion of control Lyapunov function (CLF) that is suitable for the study of forward invariance of sublevel sets. Conditions that guarantee the existence of CLF-based feedback laws inducing forward invariance of sublevel sets are established. Examples are given to illustrate the results.

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.

Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with state-depending 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.

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. © 2014 American Automatic Control Council.

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. By exploiting 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 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. ©2013 IEEE.