Overview

This chapter is devoted to extending the design methodology for SISO control systems with the highest derivative in feedback to the multi-input multi-output (MIMO) nonlinear time-varying case. In particular, the problem of output regulation is discussed, where the goals of MIMO control system design are to provide (1) output decoupling and disturbance rejection, i.e., each output should be independently controlled by a single input, and (2) the desired output transient performance indices on the condition of incomplete information about varying parameters of the plant model and unknown external disturbances. The control law structure with the relative highest derivatives in feedback is used in order to provide the desired dynamical properties globally in a specified region of the state space. A systematic design procedure for the control laws with the relative highest output derivatives in feedback is presented.

Note that throughout this chapter the problem of output regulation is discussed on the assumption that the previously presented realizability of the desired output behavior is maintained.

8.1 MIMO System without Internal Dynamics

8.1.1 MIMO System with Identical Relative Degrees

The final purpose of this chapter is a controller design methodology for MIMO nonlinear time-varying systems given by

(8.1)

(8.2)

where t is time, t ? [0, ?); X is the state vector, X = { x ₁, x ₂, ..., x _n} ^T; y is the output, y = { y ₁, y _2, ..., y _p}