Des systèmes avec des coefficients dépendant du retard ont été rencontrés dans diverses applications de la science et de l'ingénierie. Malgré la littérature abondante sur les systèmes de temporisation, il y a peu de résultats concernant l'analyse de stabilité des systèmes avec des coefficients dépendant du retard. Cette thèse est consacrée à l'analyse de stabilité de cette classe de systèmes.Les méthodes d'analyse de la stabilité sont développées à partir de l'équation caractéristique correspondante suivant une approche généralisée tau-décomposition. Étant donné un intervalle d'intérêt de retard, nous sommes capables d'identifier toutes les valeurs de retard critique contenues dans cet intervalle pour lesquelles l'équation caractéristique admet des racines sur l'axe imaginaire du plan complexe. Le critère de direction de croisement des racines sont proposées pour déterminer si ces racines caractéristique se déplacent vers le plan complexe demi-gauche ou demi-droite lorsque le paramètre de retard passe par ces valeurs de retard critique. Le nombre de racines caractéristiques instables pour un retard donné peut ainsi être déterminé. Notre analyse comprend les systèmes avec un seul retard ou des retards proportionnés sous certaines hypothèses. Le critère de direction de croisement des racines développés dans cette thèse peut être appliqués aux multiple racines caractéristiques, ou aux racines caractéristiques dont la position paramétrée par le retard est tangent à l'axe imaginaire. En tant qu'application, il est démontré que les systèmes avec des coefficients dépendant du retard peuvent provenir de schémas de contrôle qui utilisent une sortie retardée pour approcher ses dérivés pour la stabilisation. Les méthodes d'analyse de stabilité développées dans cette thèse sont adaptées et appliquées pour trouver les intervalles de retard qui atteignent un taux de convergence demandé du système en boucle fermée. / Systems with delay-dependent coefficients have been encountered in various applications of science and engineering. However, general and systematic stability analysis is rarely reported in the rich literature on time-delay systems. This thesis is committed to the stability analysis of such class of systems.Stability analysis methods are developed based on the corresponding characteristic equation following a generalized tau-decomposition approach. Given a delay interval of interest, we are able to identify all the critical delay values contained in this interval for which the characteristic equation admits roots on the imaginary axis of the complex plane. Various root crossing direction criteria are proposed to determine whether these characteristic roots move toward the left or the right half complex plane as the delay parameter sweeps through these critical delay values. The number of unstable characteristic roots for any given delay can thus be determined. Our analysis covers systems with a single delay or commensurate delays under certain assumptions. The root crossing direction criteria developed in this thesis can be applied to characteristic roots with multiplicity, or characteristic roots whose locus parametrized by the delay is tangent to the imaginary axis. As an application, it is demonstrated that systems with delay-dependent coefficients can arise from control schemes that use delayed output to approximate its derivatives for stabilization. The stability analysis methods developed in this thesis are tailored and applied to find the delay intervals that achieve a demanded convergence rate of the closed-loop system.

Les méthodologies de l'automatique ont joué au cours des dernières décennies un ´r^ole essentiel au sein de nombreux secteurs technologiques avancées. Cependant, de nombreuse questions restent ouvertes. Parmi celles-ci, celles concernant la stabilité et la stabilisation de systèmes non linéaires sont d'intérêt primordial. Afin de stabilizer un système (physique ou non), il est nécessaire de capter et interpreter en temps réel les informations hétérogènes caractérisant son fonctionnement afin intervenir efficacement. Actuellement ces informations ne sont pas captées en temps continu, mais de façon synchrone ou asynchrone et ceci est valable aussi pour les actuateurs. De façon très naturelle, on définit donc un système hybride, caractérisé par des dynamiques à la fois discrètes et continues. Dans ce contexte, cette thèse est orientée au développement de nouvelles méthodologies pour la stabilisation de systèmes échantillonnés non linéaires en se focalisant sur la stabilisation de formes cascades qui se retrouvent dans de nombreuse situations concretes. Pour cela, on étudiera l'effet de l'échantillonnage sur les propriétés de la dynamique continue et l'on proposera des méthodologies pour la conception de lois de commande qui ne requièrent pas d'assumptions supplémentaires au cas continu.Enfin, on étudiera l'effet de l'échantillonnage sur des systèmes présentant de retards sur les entrées. On développera des lois de commande stabilisantes exploitant la structure en cascade induite par l'échantillonnage. Des exemples académiques illustreront les calcules des solutions et leur performances tout au long du manuscript. / Over the last decades the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model.Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system. Academic examples will illustrate the computational aspects together with their performances throughout the whole manuscript.

Very little research has occurred about students with severe disabilities and verbal difficulties and their ability to learn phonics, decoding, and other early literacy skills(Ainsworth et al., 2016 and Johnston et al., 2009b). Ainsworth et al. (2016) used the Accessible Literacy Learning curriculum to teach phonics and decoding. Johnston et al. (2009b) used a three-step instructional strategy, step one - increased opportunities for adult-directed teaching and active teacher child interaction, step two- use of time delay to teach, step three-consequences, to teach phonics and decoding. While both studies utilized time delay in some fashion, they were not entirely based upon the evidence-based practice. Therefore, the purpose of this study is to determine whether constant time delay is effective in teaching phonics and decoding to students with severe disabilities and verbal difficulties and if students can generalize the skill to words that have not been explicitly taught. Results indicated a functional relation between the use of constant time delay and decoding of CVC words. Additionally, students were able to maintain and generalize learning. Students with severe disabilities and verbal difficulties can effectively learn decoding of CVC words through constant time delay and can maintain and generalize the skill. Results were similar to other studies which implemented constant time delay to promote emergent literacy skills (e.g., Browder et al., 2012; Dessemont et al., 2019; Spooner et al., 2015; Tucker Cohen et al., 2008). Practitioners can use constant time delay to teach decoding to students with severe disabilities and verbal difficulties and to promote early reading skills. Future research should replicate the study with students from different age groups as well as examining the effects of this strategy on the acquisition of CCVC and CVCC words.

Synchronization of distributed time difference of arrival (TDOA) sensor networks can be performed using reference signals from GPS satellites. This method provides high accuracy, but is vulnerable to jamming, and is not reliable enough to be used in military applications. A solution that does not depend on any signals transmitted from external actors is preferred. One way to achieve this is to use reference signals transmitted from a UAV. A UAV is suitable since only local synchronization for a geographically restricted area is necessary. The local synchronization is achieved by estimating the time-delay between the transmission and reception of a reference signal. The estimated time-delay can be used to detect drifts in the clocks of the TDOA sensors. This thesis analyzes com- mon reference signals, to evaluate which provide high accuracy for time-delay estimation, and what properties of the signals influence the estimation accuracy the most. The simulations show that the time-delay estimation performance can reach the same accuracy as synchronization against GPS for different types of signals. An increased bandwidth is more important than an increased signal length or signal-to-noise ratio to improve the estimation accuracy.

The continual increase of wireless technologies in the world has motivated the use of phased arrays to mitigate radio frequency interference (RFI). There are many methods of performing beamforming for RFI rejection, but they are traditionally physically large and complicated solutions. Phased arrays need to be shrunk and made cheaper for them to see widespread use. This work presents several compact phased array receivers for different applications. The first part of this thesis presents a software GPS processor for a digital beamforming GPS receiver. The receiver is small enough to be flown on drones and enables GPS signals to be processed and a user’s position to be determined. Using digital beamforming, it can operate even under poor conditions such as intentional jamming, RFI, and large multipath effects. Next, this work builds a frontend RF chain for a true time delay phased array receiver. The receiver uses analog true delay delay chips to mitigate radio frequency interference in sensitive instruments. True time delay allows for analog beamforming over a wide bandwidth, but compact true time delay solutions are new and untested. The receiver allows these solutions to be properly vetted in a full system. The chain uses novel compact wideband antennas for L-band frequencies and traditional low cost amplifiers and filters. The last section of this thesis updates the open-source CASPER project to fully support RF system-on-chips. CASPER is an open-source framework for radio astronomy instruments. It speeds up the design and implementation of radio astronomy instruments on compact platforms and makes them easier to interact with. This work expands the framework to use the transmit abilities of advanced RF system-on-chip platforms. With this expansion, full duplex systems such as communications and radar can now also use CASPER. A full loopback beamforming test built on CASPER demonstrates both transmit and receive beamforming.

The purpose of this study was to examine the effects of constant time delay on decoding letter sounds within consonant-vowel-consonant words and to read constant-vowel-constant words skills for students with severe disabilities and verbal difficulties. This study used a multiple probe across participants design with four students with severe intellectual and/or development disabilities. Results indicated a functional relation between the use of constant time delay and decoding of CVC words. Additionally, students were able to maintain and generalize learning. Results were similar to other studies which implemented constant time delay to promote emergent literacy skills. Practitioners can use constant time delay to teach decoding to students with severe disabilities and verbal difficulties and to promote early reading skills. Future research should replicate the study with students from different age groups as well as examine the effects of this strategy on the acquisition of CCVC and CVCC words.

A dynamical system's state evolves over time, and when the system stays near a particular state this state is known as a stable state of the system. Through control methods, dynamical systems can be manipulated such that virtually any state can be made stable. Although most real systems evolve continuously in time the application of digital control methods to these systems is inherently discrete. States are sampled (with sensors) and fed back into the system in discrete-time to determine the input needed to control the continuous system. Additionally, dynamical systems often experience time delays. Some examples of time delays are delays due to transmission distances, processing software, sampling information, and many more. Such delays are often a cause of poor performance and, at times, instability in these systems. Recently a criterion referred to as intrinsic stability has been developed that ensures that a dynamic system cannot be destabilized by delays. The goal of this thesis is to broaden the definition of intrinsic stability to closed-loop systems, which are systems in which the control depends on the state of the system, and to determine control parameters that optimize this resilience to time delays. Here, we give criteria describing when a closed-loop system is intrinsically stable. This allows us to give examples in which systems controlled using Linear Quadratic Regulator (LQR) control can be made intrinsically stable.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

Task allocation, and task switching have an important effect on the efficiency of distributed, locally controlled systems such as social insect colonies. Both efficiency and workload distribution are global features of the system which are not directly accessible to workers and can only be sampled locally by an individual in a distributed system. To investigate how the cost of task switching affects global performance we use social wasp societies as a metaphor to construct a simple model system with four interconnected tasks. Our goal is not the accurate description of the behavior of a given species, but to seek general conclusions on the effect of noise and time delay on a behavior that is partitioned into subtasks. In our model a nest structure needs to be constructed by the cooperation of individuals that carry out different tasks: builders, pulp and water foragers, and individuals storing water. We report a simulation study based on a model using delay-differential equations to analyze the trade-off between task switching costs and keeping a high degree of adaptivity in a dynamic, noisy environment. Combining the methods of time-delayed equations and stochastic processes we are able to represent the influence of swarm size and task switching sensitivity. We find that the system is stable for reasonable choices of parameters but shows oscillations for extreme choices of parameters and we find that the system is resilient to perturbations. We identify a trade-off between reaching equilibria of high performance and having short transients.

A single subject alternating treatment design was used to compare the relative effectiveness of one-to-one embedded instruction in the general education classroom and one-to-one massed practice instruction in a special education class. Four middle school students with developmental disabilities, their special education teacher, and paraprofessional participated in the study. The results indicate that embedded instruction is an effective instructional strategy for students with developmental disabilities being served in inclusive settings. However, the results indicate that there was some difference in the efficiency of the two instructional formats. Two students reached criterion more rapidly in the one-to-one massed instructional intervention while the one-to-one embedded instruction was more efficient for one student. There was no difference between the interventions for the fourth student. Finally, the study validated previous research that found that both special education teachers and paraprofessionals can, with minimal training, accurately implement embedded instructional interventions in the general education classroom. Implications for practitioners and researchers are discussed.