For control theory from a mathematician, Fleming, long at the Division of Applied Mathematics at Brown University, there is: Wendell H. Fleming and Raymond W.

For control theory from a mathematician, Fleming, long at the Division of Applied Mathematics at Brown University, there is: Wendell H. Fleming and Raymond W. Rishel, Deterministic and Stochastic Optimal Control, ISBN 0-387-90155-8, Springer-Verlag, Berlin, 1979. There is more on optimization, especially from the Hahn-Banach theorem, and also Kalman filtering, in David G. Luenberger, Optimization by Vector Space Methods, John Wiley and Sons, Inc., New York, 1969.