A novel approach to control of nonminimum-phase nonlinear systems

We present an approach to control of nonminimum-phase multiple-input-multiple-output (MIMO) nonlinear systems based on a singular perturbation-like technique. First, we show that a MIMO nonlinear system can be converted into a singularly perturbed system through magnitude and time-scaling transformation. In particular, the proposed transformation technique can make the hidden or internal dynamics behave like a fast subsystem. However, the fast subsystem takes a weakly controllable form, which implies that a small positive low-gain parameter multiplies the control input in the fast subsystem. For this reason, the well-known integral manifold approach is then utilized to decompose the resulting singularly perturbed system into two subsystems in separate timescales, each of which is of a lower dimension and, more importantly, controllable in the sense that the control input will explicitly appear in the boundary-layer system. The proposed method is particularly useful to make the input-output dynamic characteristics of a decouplable nonminimum-phase nonlinear system decoupled and linear.