Dan Barag and David Flusser, in their article concerning an ossuary bearing the names "Yehohanah" and "Theophilus", write, "After playing an important role in public life during the time of Cumanus (50-52 C.E.), he [Jonathan, Theophilus' brother] was murdered at the instigation of the prefect Felix” (D. Barag and D. Flusser, "The Ossuary of Yehohanah Granddaughter of the High Priest Theophilus", Israel Exploration Journal, 36 , 43n.19; they reference Schurer, The History of the Jewish People in the Age of Jesus Christ, rev. ed. [Vermes and Millar], 230).
Is this perhaps why Luke casts Felix in such a wicked light in Acts? Felix is said to have expected a bribe from Paul (Ac24.26). If indeed Felix was responsible for the murder of Theophilus' brother Jonathan, then his holding of Paul (cf. Ac24.27) might very well be (spiteful?) motivation for Theophilus to intervene on Paul's behalf. Perhaps Luke, knowing of Felix responsibility in Jonathan's death, hoped to instigate intervention on the part of Theophilus.
(I have read that Jonathan was actually killed by the Sicarii, though the event was instigated by Felix. The citation eludes me at present.)