In this paper, a new indirect adaptive control method is presented. This method is based on a lifted representation of the plant that can be stabilized using a simple performant periodic control scheme. The controller parameters computation involves the inverse of the controllability/observability matrix. Potential singularities of this matrix are avoided by means of an appropriate estimates modification. This estimates transformation is linked to the covariance matrix properties, and hence, it preserves the convergence properties of the original estimates. This modification involves the singular value decomposition of the controllability/observability matrix's estimate. As compared with previous studies in the subject, the controller proposed here does not require the frequent introduction of periodic n-length sequences of zero inputs. Therefore, the new controller is such that the system is almost always operating in closed loop, which should lead to better performance characteristics.