Nonlinear Control Sy.. - Free

30 CHAPTER 1. INTRODUCTION
Notes and References
We will often refer to linear time-invariant systems throughout the rest of the book. There
are many good references on state space theory of LTI systems. See, for example, references
[15], [2], [64], or [40]. Good sources on phase-plane analysis of second-order systems are
References [32] and [59]. See also Arnold [3] for an excellent in-depth treatment of phaseplane
analysis of nonlinear systems. First-order systems are harder to find in the literature.
Section 1.4 follows Strogatz [76]. The literature on chaotic systems is very extensive. See
Strogatz [76] for an inspiring, remarkably readable introduction to the subject. Section
1.8 is based mainly on this reference. Excellent sources on chaotic dynamical systems are
References [26], [22] and [58]. The magnetic suspension system of Section 1.9.1 is a slightly
modified version of a laboratory experiment used at the University of Alberta, prepared by
Drs. A. Lynch and Q. Zhao. Our modification follows the model used in reference [81].
The pendulum-on-a-cart example follows References [9] and [13]. Our simple model of the
ball-and-beam experiment was taken from reference [43]. This model is not very accurate
since it neglects the moment of inertia of the ball. See Reference [28] for a more complete
version of this model.