Are switched systems (with switchings in time) well posed (Hadamard) in the sense that the solution exists, is unique and continuously depends on initial conditions?
Accurate references are needed in the particular cases of continuous dependence upon initial conditions.
Thank you.
Dear Israel, I hope that attached paper (from Udine University, Italy) is useful for you.
Gianluca
Dear Israel, if switching is a function of time, then the system (either linear or nonlinear) would reduce to a unique dynamics with a further dependence wrt time, with values in a discrete set. Thus, if the switching remains measurable wrt time, the system satisfies Caratheodory's assumptions, and hence has a unique solution, which depends continuously on the initial state.
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