CHAPTER TWO
TRACKING AND DISTURBANCE REJECTION FOR NONLINEAR SYSTEMS
In this chapter we derive a method to achieve tracking and
disturbance rejection for certain nonlinear multi-input, multi-output
systems. Conditions are given which reveal when the problem can be
solved. An internal model system is used as a basis for the design,
however, unlike the case of the linear system, the internal model
contains dynamics which may not appear in either the reference or
disturbance signals.
Notation
Given a positive integer n, let Rn denote the set of n-dimensional
vectors with elements in the reals and let Rmxn be the set of matrices
of dimension mxn with elements in the reals. The symbol II II shall
denote the Euclidian norm of a given vector. For a matrix A, the symbol
llAll^ will be the induced norm defined as
Vz
HAII- := sup llAxll = [X (A'A)] (2-1)
1 lixii=l max
The symbol := will mean equality by definition and the notation A1
signifies the transpose of the matrix A.
When referring to square matrices, the notation A>0, A > 0 A<
0 will mean that A is positive definite, positive semidefinite, and
negative definite respectively.
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