AbstractThe explicit self‐tuning control of linear systems with constant but unknown parameters is analysed. The class of single‐input/single‐output, discrete‐time stochastic systems with coloured noise is considered without imposing a minimum‐phase condition. A stochastic approximation type of identification algorithm coupled with a general linear control law structure satisfying weak conditions is shown to lead to the required stability properties of the closed‐loop system. Similar approaches have been previously proposed for deterministic systems and for stochastic systems with uncorrelated disturbances. The specific example of a pole‐shifting algorithm is considered and it is shown that the required asymptotic behaviour is achieved under certa
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