This article presents an alternative ac-ac converter topology and its control for low-speed three-phase induction motor drives fed from single-phase ac mains. The proposed matrix converter based drive system eliminates the dc link capacitor, thus facilitating high power density and system reliability. The primary challenge in controlling a 1φ to 3φ matrix converter is to navigate the discrepancy of instantaneous power across the 1φ grid and 3φ load via a direct ac-ac converter. In order to address this concern, it is proposed to use mathematical modeling of the motor and input LC filter for state selection, in order to deliver improved current waveforms. Enhanced performance is demonstrated through simulations, and further validated using experimental results. Particularly improved power quality performance is achieved at low motor speeds, where precise low-speed sensorless operation is ensured through suitable speed observer.