
Joel H. Shapiro 

Abstract: This
paper studies autonomous, singleinput, singleoutput linear
control systems on finite time intervals. The object of interest
is the output operator, which associates to each
input function and initial state vector the corresponding system
output. Main result: If the system has relative degree r, then for any "admissible" Banach space of inputs U, the output operator takes U x C^n boundedly onto the "Sobolev space" of complexvalued functions f in C^(r1)([0, T ]) for which the rth order derivative f^(r) is absolutely continuous, with f (r) in U.This completes recent results of Jonsson and Martin (J. Math. Anal. App. 329 (2007), 798821) who showed that if the system is minimal and U is either L^2([0, T ]) or C([0, T ]), then the output operator is continuous, with range dense in U. 
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