Before carrying out a design, we must analyze the realizability of the desired output behavior. In the preceding chapters attention was devoted to the problem of control system design with the highest derivative in the feedback loop for the SISO plant model given by (4.27), where output regulation with prescribed dynamics may be provided if the condition (4.35) holds. This chapter is devoted to consideration of conditions that allow us to provide desired output behavior for more general dynamic systems. It will be shown that, in general, the analysis of the realizability of the desired output behavior is a much more complicated problem, and involves such concepts as invertibility of a dynamic system, nonlinear inverse dynamics, and internal behavior analysis of the system. In this chapter, concepts such as invertibility index (relative degree), normal form of nonlinear systems, internal stability analysis, degenerated system on the condition of output stabilization, and zero-dynamics are discussed. Finally, the design procedure for SISO nonlinear control systems is discussed in the presence of internal dynamics.

7.1 Control Problem Statement for MIMO Control System

7.1.1 MIMO Plant Model

Let us consider a nonlinear time-varying system in the following form:

(7.1)

(7.2)

where

• t denotes time, t ? [0, ?);

• X is the state vector, X = { x ₁, x ₂, , x _n} ^T;

• X(0) = X ₀ is the initial state, X ₀ ? ? _X, ? _X is a...