An impulsive dynamical systems framework for reset control systems |
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Authors: | Alfonso Baños Juan I Mulero Antonio Barreiro Miguel A Davó |
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Affiliation: | 1. Departamento de Informática y Sistemas, Universidad de Murcia, Murcia, Spain;2. Departamento de Ingeniería Sistemas y Automática, Universidad Politécnica de Cartagena, Cartagena, Spain;3. Departmento Ingeniería de Sistemas y Automática, Universidade de Vigo, Vigo, Spain |
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Abstract: | Impulsive dynamical systems is a well-established area of dynamical systems theory, and it is used in this work to analyse several basic properties of reset control systems: existence and uniqueness of solutions, and continuous dependence on the initial condition (well-posedness). The work scope is about reset control systems with a linear and time-invariant base system, and a zero-crossing resetting law. A necessary and sufficient condition for existence and uniqueness of solutions, based on the well-posedness of reset instants, is developed. As a result, it is shown that reset control systems (with strictly proper plants) do not have Zeno solutions. It is also shown that full reset and partial reset (with a special structure) always produce well-posed reset instants. Moreover, a definition of continuous dependence on the initial condition is developed, and also a sufficient condition for reset control systems to satisfy that property. Finally, this property is used to analyse sensitivity of reset control systems to sensor noise. This work also includes a number of illustrative examples motivating the key concepts and main results. |
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Keywords: | Impulsive dynamical systems reset control systems hybrid systems |
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