This paper deals with the synthesis of a suboptimal controller, based on the solution of the algebraic Riccati equation (ARE). The numerical procedure for obtaining the solution is presented. In applications the controlled system parameters often differ from the ones used in the ARE. In this case the optimality of the control system and even its stability are questionable. Therefore, it would be very useful to design an adaptive linear suboptimal controller. Such a controller should be able to detect changes in the system parameters and adjust its parameters.