On the stability of a self-tuning controller in the presence of bounded disturbances

A proof of bounded-input bounded-output stability of a discrete-time self-tuning control system in the presence of bounded disturbances is given. A recursive least-squares with a dead zone is utilized in the parameter estimation scheme, so that self-tuning takes place only when the identification error exceeds a certain threshold. The controller minimizes a quadratic cost function so that the control signal fluctuations are penalized. The controller can deal with nonminimum-phase systems, which is significant because the nonminimum-phase cases often occur in discrete-time systems. The upper bound of tracking error is also given