A fast state-space self-tuner is developed for suboptimal control of linear stochastic multivariable systems. The suboptimal self-tuner is determined by utilising both the standard recursive-extended-least-squares parameter estimation algorithm and the recently developed matrix sign algorithm, which gives a fast solution of the steady-state discrete Riccati equation. The developed suboptimal state-space self-tuner can be applied to a class of stable/unstable and minimum/non-minimum phase linear stochastic multivariable systems, in which the pair (A, C) is block observable and the pair (A, B) is stablisable. Also, the pair (A, Q̂) withQ̂Q̂T=Qis detectable whereA, BandCare system, input and output matrices, respectively, andQis a weighting matrix in a quadratic performance index.