An impulsive dynamical systems framework for reset control systems

作者：Banos Alfonso^*; Mulero Juan I; Barreiro Antonio; Davo Miguel A

来源：International Journal of Control, 2016, 89(10): 1985-2007.

DOI：10.1080/00207179.2016.1146969

• Impulsive dynamical systems
• reset control systems
• hybrid systems

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.

• 出版日期2016