Design of a globally stable direct adaptive VSS regulator for multivariable nonminimum-phase systems based on the doubly coprime factorization

An adaptive regulator problem for continuous-time multivariable nonminimum-phase systems of unknown order is considered using the idea of the sliding mode control method. Introducing the augmented state variable filters of an input, an output and an auxiliary input and taking an advantage of the doubly coprime factorization associated with the system transfer matrix, an adaptive state feedback control scheme is proposed that drives these augmented state variables to the subspace defined by the intersection of the two sliding hyperplanes on which the state variables decay to the origin exponentially quickly. The global asymptotic stability of the proposed adaptive regulator is established under the assumption that the upper bound of the controllability index is known