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.
Notati on
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 ifAni will be the induced norm defined as
i
IIAIIi : sup oAxi = Exmax (AA)] (2-1)
The symbol := will mean equality by definition and the notation A' 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.