This paper presents an analytical study of an input current-mode control based on a linear matrix inequalities (LMI) for a non-inverting buck-boost converter. The LMI control technique makes better the dynamic response of this converter in comparison with previous research works, where its currents has been regulated using a classical analogue PI controller with an additional pole. The main features of the selected converter are its voltage step-up and step-down properties, high efficiency, wide bandwidth and low input and output current ripples. All of these converter's properties allows it to be used as a modular converter capable of being positioned at any converter locations in hybrid systems, which are formed by varying-voltage-sources, current controlled dc-dc converters and auxiliary storage devices such as batteries or capacitors. The designed state-feedback controller has the following aims, among others: pole placement constraints, control effort limitation, and decay rate and bandwidth improvement. The use of state-space averaging (SSA) method allows to describe LMI constraints which guarantees stability and provide good performances under a close loop pole region and control signal bound. The theoretical analysis have been simulated by means of Matlab and PSIM on an 800-W coupled-inductor buck-boost dc-dc switching converter.