Adaptive regulation of multivariable nonminimum phase systems based on the sliding mode control method

A design method for constructing the adaptive regulator of a multivariable nonminimum-phase system has been developed via the sliding mode control approach where two kinds of sliding hyperplanes are simultaneously generated. The auxiliary inputs and the system input generating the sliding hyperplanes have been determined and the error equations for estimating unknown feedback gains have been derived. Then by constructing the Lyapunov function associated with the strictly positive real transfer function of the error system, the asymptotic stability of the proposed adaptive regulator has been established. This adaptive regulator may prove to be robust to system disturbances and parameter variations provided that the sliding modes are properly maintained by the auxiliary inputs v₁ and v₂