Generalized Volterra theory in control systems analysis

In the analysis of nonlinear systems by means of the Volterra series theory, there are two schools: namely, the time domain approach by Barret and the transform domain approach by Brilliant, George and Lubbock. The fundamental difficulty involved in the transform approach is how to perform the multiple dimensional inverse Laplace transform. George uses the method of inspection while Lubbock develops the associate variable technique. In this dissertation, several new theorems are developed for the associate variable theory. A unified and systematic procedure is obtained. This enables us to generate associated transform pairs freely. In the time domain approach, a generalized theory, or the method is established. It is an iterative scheme which is simple in derivation, effective in calculation and computer-oriented. The way to treat the initial conditions in the approach is original. Several nonlinear system examples are solved and analyzed for illustrating and demonstrating the power and simplicity of the generalized Volterra theory.