Removal of a positive realness condition in minimum variance adaptive regulators by multistep horizons

Convergence properties of a new class of adaptive regulators based on multistep quadratic cost functionals are analyzed by Ljung´s ODE method. It is shown that, if the time horizon of the controller is large enough, the MV feedback law is a possible convergence point of the algorithm, even if the plant does not satisfy a positive realness condition.