Abstract
This paper considers switched dynamical systems with state-space dilation and contraction formed by concatenating the states of a set of local dynamical systems or semi-flows on state spaces with different dimensions at specified time-instants. These systems arise naturally in many aerospace applications such as multi-body dynamic systems involving changes in the degrees of freedom, and systems composed of multiple spacecraft with docking and undocking capabilities flying in formation. The notions of stability of invariant sets in the sense of Lyapunov for usual dynamical systems are extended to this class of switched dynamical systems. Also the notion of finite-time stability with specified bounds is introduced. Sufficient stability conditions are established for a special class of switched dynamical systems with state-space dilation and contraction. Their application to spacecraft formation stability analysis is discussed.
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