Control of a class of multivariable nonlinear systems without vector relative degrees: a backstepping approach

A new control approach for a class of multivariable nonlinear systems whose decoupling matrix is singular is presented. For this class of systems, local decoupling may be achieved by dynamic compensation. Instead of decoupling the nonlinear system by adding chains of integrators in the input channels, we modify the dynamic extension algorithm by incorporating backstepping design methods to partially close the loop in each design step. The resulting control law by this new approach is a static state feedback law. Although the final closed loop form of the nonlinear system is not decoupled, each output is controlled to the desired value asymptotically. A design example is given to illustrate this approach