Criterion of the relative degree applied to design of multivariable systems

The question, whether and when the criterion of the relative degree equal to one (RD1), may be applied for designing a multivariable system, is analyzed in the paper. The criterion is commonly utilized in sliding mode control in the case of the plants with single input and single output (SISO). For the multivariable case, first the decoupling of the fast transients is proposed, basing on a conversion of the matrix transfer function (MTF) description of the plant. Then, the controllers with high gain and derivatives are designed separately for each plant output, using the criterion RD1. It is noticed that the same approach may be applied for the multivariable systems with sliding mode control. It is noticed that both the multivariable systems: continuous with control saturation and relay with sliding mode control are in some sense equivalent. The considerations of the paper are confirmed by the performed simulations.