Robust multivariable implicit self-tuning control

A robust multivariable linear quadratic implicit self-tuningalgorithm is presented. It is shown that the closed-loop outputerror is bounded for multiplicative modelling uncertainty, providedthat all the unstable zeros of the plant are captured in thenominal model. The algorithm can be applied to nonminimum-phasesystems, and does not require the explicit solution of the algebraicmatrix polynomial equation. The controller parameters are directlyestimated from two implicit prediction models which containthe plant and controller parameters in bilinear form. The stability analysis is performed by applying conic-sectortheory to a new error equation which is decomposed into twocomponents embodying a linear and non-linear operator, namelythe modelling uncertainty and the parameter estimator respectively.Simulation results are presented to demonstrate the performanceof the proposed adaptive controller.