Elementary Theory of Nonlinear Feedback for Multi-Input Multi-Output Systems

In this Chapter we shall see how the theory developed for single-input single output systems can be extended to nonlinear systems having many inputs and many outputs. As a matter of fact, we shall see that a straightforward extension of most of the design procedures illustrated so far is possible, provided we restrict our consideration to a particular class of multivariable nonlinear systems, that will be specified in a moment. For multivariable nonlinear systems not belonging to this class, the solution of some important design problems like exact linearization, asymptotic stabilization, disturbance decoupling and noninteracting control requires more sophisticated techniques and will be treated separately in the next two Chapters.