One group of approaches involves replacement of the nonlinear system by (in some sense) a linear approximation. Analysis of the linear system then gives information about the original nonlinear system. The describing function method and Lyapunov's first method are in this group. A second approach attempts to find useful information about a system without solving the system equations. Lyapunov's second or direct method has such an approach to determine approximate regions of stability. A third approach uses what I have called 'envelope techniques'. Here, the nonlinearity is enveloped graphically in a linear segment and a 'worst-case' stability analysis is then possible. Numerical solution of nonlinear equations is, of course, always possible but is of limited usefulness in obtaining an overall insight into system behaviour. A useful graphical technique for the display of nonlinear system behaviour is the phase-plane. Despite the fact that the display is virtually restricted to second-order systems, it allows most of the important concepts of nonlinear analysis to be illustrated.

Inspec keywords: Lyapunov methods; nonlinear control systems; linear systems; nonlinear equations; stability

Other keywords: nonlinear system; nonlinear control theory; Lyapunov method; linear approximation; worst case stability analysis; nonlinear equations; phase plane; linear system; envelope techniques

Subjects: Nonlinear control systems