ABSTRACT
This chapter argues that optimization can be used to solve the design problem completely. The case for optimization becomes stronger when one moves outside the class of linear systems. Design of controllers for nonlinear systems is at a less advanced state despite recent spectacular progress due to the complexity and variety of the systems encountered in practice. In practice, of course, controllers are nearly always nonlinear, even if designed using linear theory. The work involved in constructing a Lyapunov function for a given autonomous system is comparable to that of determining a nonlinear feedback law. The first requirement for a design environment is a facility for simulating the system and its controller, together with a suitable friendly interface for inputting the system descriptions and modifying them. Because the need to assess stability may recur frequently in the design process, it appears necessary to avoid repeated modification of the Lyapunov function.
